determination of natural radioactivity concentrations in soil

Determination of Natural Radioactivity Concentrations in Soil a comparative study of

Windows and Full Spectrum Analysis

by

Katse Piet Maphoto

Thesis submitted in partial fulfillment of the

requirements for the MSc degree in Physics at the

University of the Western Cape

August 2004

Supervisor Prof R Lindsay

Co-supervisor Dr RT Newman (iThemba LABS)

Declaration

I the undersigned declare that the work contained in this thesis is my own original work and

has not previously in its entirety or in part been submitted at any university for a degree

Signature

Date

ii

Acknowledgements

I am greatly indebted to the following people who made this thesis possible

Prof Robbie Lindsay supervisor for the help in financing my studies and guiding me every

step of the way especially with challenging aspects such as programming

Dr Richard Thomas Newman co-supervisor for the guidance and suggestions especially

during the writing up of the thesis

iThemba LABS for financing and granting me the opportunity to do my study with them

and to all the staff from the library to the Human Resource for their support

To my parents Magate le Baboloki for always being on my side whenever I needed them

and for their love and patience and my Family for their support and endless love

Environmental Radioactivity Group Dawid de Villiers Angelo Joseph Raphael Damon

and Lerato Sedumedi (former Technical Officer) for their helpful discussions

To Prof Rob de Meijer from the Kernfysisch Versneller Instituut (KVI) in the Netherlands

for helpful discussions and suggestions

To Peane Maleka former masters student at the iThemba LABS for introducing me to the

basic concepts of experimental methodologies

UWC Physics department for making me feel at home when I felt like a stranger and all my

colleagues for their encouragement

Finally thanks to the Almighty God the Creator of the Universe the Alpha and Omega for

keeping me alive and kicking all the way

iii



Katse Piet Maphoto

Abstract

In this study two methods of analysing activity concentrations of natural radionuclides (238U 232Th and 40K) in soil are critically compared These are the Window Analysis (WA) and Full

Spectrum Analysis (FSA) In the usual WA method the activity concentrations are determined

from the net counts of the windows set around individual γ-ray peaks associated with the

decay of 238U 232Th and 40K In the FSA method the full energy spectrum is considered and

the measured spectrum is described as the sum of the three standard spectra (associated with 238U 232Th and 40K respectively) each multiplied by an unknown concentration The

concentrations are determined from the FSA and correspond to the activity concentrations of 238U 232Th and 40K in the soil The standard spectra derived from separate calibration

measurements using the HPGe detector represents the response of the HPGe to a Marinelli

sample beaker containing an activity concentration of 1 Bqkg

A χ2 -minimisation procedure (for the FSA method) is used to extract the accurate activity

concentrations The results of this technique (FSA) were obtained and compared with the

conventional (WA) method of analysis Although a good correlation was found between

results from these methods the disadvantage was with the self-absorption effects which result

into poor fit (especially at the continuum) This proved to have had an impact on the measured

results for FSA This phenomenon was carefully studied and a recommendation is made in the

conclusion

Five samples having a range of activity concentrations (relative and absolute) and densities

were analyzed as part of this study In one case (that for the (stearic acid + 232Th) sample) the

absolute activity concentration of 232Th in the sample was known The samples were measured

iv

for longer times (about 8 to 10 hours) and short times (about 1 hour) Activity concentrations

were then calculated from each spectrum using WA and FSA For the long measurements the

ratio of WA-determined concentrations to FSA-determined concentrations varied between

about 10 and 13 for 238U between 10 and 16 for 232Th and between 097 and 10 for 40K

The corresponding ratio for short measurements varied between 10 and 12 for 238U between

07 and 11 for 232Th and between 09 and 10 for 40K

This is with the exception of the low activity sample of the West coast sample which gave the

ratios ranging from 097 to 16 in the case of long measurement and 14 to 74 in case of the

short measurements

In the case of the (stearic acid + 232Th) sample the WA and FSA determined activity

concentrations deviated from the expected concentrations by 9 and 21 respectively

This study demonstrated that the FSA technique could be useful for extracting activity

concentrations from high-resolution gamma ray spectra in a relatively straightforward and

convenient way provided that proper consideration is given to effects associated with sample

volume and density in relation to the sources used to generate standard spectra

v

Table of Contents

CHAPTER 1 Introduction 1

11 The atomic nuclei and radioactivity overview2

111 Radioactive decay3

112 Decay modes3

113 Decay rates5

12 Types of environmental radioactivity6

13 Review of primordial radioactivity7

131 Decay series of natural radionuclide7

14 Literature review natural radionuclide activity concentrations in soil12

141 Methods used to determine activity concentrations in soil13

142 Interactions of gamma rays with matter14

1421 Photoelectric absorption14

1422 Compton scattering15

1423 Pair production17

1424 Attenuation Coefficients18

143 Examples of gamma ray spectrometry systems19

vi

15 The motivation for this study21

16 The aim and scope for this study23

17 Thesis outline24

CHAPTER 2 Experimental Methods25

21 The HPGe gamma-ray detection facility25

211 Physical layout26

212 HPGe technical specifications28

213 Electronics28

214 Figure of merit34

22 Sample Selection Preparation and Measurement41

23 Reference Sources43

24 Data Acquisition44

CHAPTER 3 Data Analysis46

31 Window Analysis46

311 Determination of γ-ray detection efficiency49

312 Treatment of uncertainties in WA 62

32 Full Spectrum Analysis64

vii

321 Derived standard spectra64

322 Chi-square minimisation technique70

323 Treatment of uncertainties for FSA86

CHAPTER 4 Results and Discussion88

41 WA Results88

42 FSA Results97

43 Comparison of WA and FSA Results99

44 Discussion of WA Results110

45 Discussion of FSA Results111

CHAPTER 5 Conclusion119

51 Outlook119

APPENDICES

A-1 Some Formulae for Combining uncertainties121

A-2 Means and Standard deviation122

B FORTRAN program125

C Background Spectrum127

D Self-absorption effects128

viii

E Ratios of activity concentrations133

ix

List of Tables

1-1 Amount of naturally occurring radionuclides in typical soil of a volume 1 km times 1 km and

1 m deep 12

1-2 Characteristic radiometric fingerprints of sand and mud 13

1-3 Radiometric fingerprint given as activity concentrations (Bqkg-1) associations with

heavy minerals in South Africa 22

2-1 γ-ray energies with associated Full Width at Half Maxima (FWHM) for γ-ray lines

associated with the decay of 40K and the series of 232Th and 238U used for energy

calibrations 35

2-2 A table of counts in the chosen region of interest with number of channels along the 60Co Compton continuum and in the channel corresponding to the highest number of

counts in the full energy peak 40

2-3 The table of samples collected at different sites 41

2-4 The table shows data on the reference material used 44

2-5 Spectral information on reference sources 45

2-6 Spectral information on Samples and background 45

3-1 The gamma ray lines used and their associated branching ratios 52

4-1 The activity concentration results for the Kloof sample number 6 by WA method 88

x

4-2 The activity concentration results (long measurement) for the Westonaria sample

number 17A by WA method 89

4-3 The activity concentration results (long measurement) for the West Coast sample

number 3 by WA method 90

4-4 The activity concentration results for (long measurement) the Brick clay sample


4-5 The activity concentration results for (long measurement) the thorium + stearic acid

sample number 5 by WA method 92

4-6 The activity concentration results (short measurement) for the Kloof sample number 6

by WA method 93

4-7 The activity concentration results (short measurement) for the Westonaria sample


4-8 The activity concentration results (short measurement) for the West Coast sample


4-9 The activity concentration results (short measurement) for the Brick clay sample


4-10 The FSA results (8-10 hours measurements) uncertainties and the associated chi-square

per degree of freedom obtained using a cut off energy of 300 keV for the samples

indicated 97

xi

4-11 The FSA result (one hour measurement) uncertainties and the associated chi-square


indicated 98

4-12 The activity concentration from the two methods of analysis for long measurements 99

4-13 The activity concentration from the two methods of analysis for short time

measurement 100

4-14 Advantages and disadvantages for the two methods including the optimum

measurement times required for the activity concentration determination 108

4-15 The results for sample 5 a high thorium content sample 109

A-1 The table shows some of the equations used in the calculation of the uncertainty ∆R

121

D-1 Results of calculations of the effective thickness t for two Marinelli beaker volumes 130

D-2 A table of the mass attenuation coefficients and the transmission factors 131

D-3 The dimensions of the full and half-full Marinelli beaker 132

E-1 The ratios of the activity concentrations (WAFSA) for samples used in the study

the ratios are shown for both short and long measurement 133

xii

LIST OF FIGURES

1-1 40K decays by β- and electron capture to 40Ar and 40Ca 8

1-2 A Z-A Plot indicating how the 238U nucleus decays the half-lives for the respective

nuclides are indicated 9

1-3 A Z-A Plot indicating how the 232Th nucleus decays the half-lives for the respective


1-4 The schematic representation of the mechanism of photoelectric absorption where a γ-

ray with energy Eγ interacts with a bound electron 14

1-5 The diagrammatic representation of emission of fluorescent X-rays 15

1-6 The diagrammatic illustration of mechanism of Compton scattering 16

1-7 The diagrammatic illustration of pair production 17

1-8 The linear attenuation coefficient of germanium and its component parts on a log-log

scale 19

1-9 Application of Radiometric methods in different fields 21

2-1 The picture showing the setup of the Environmental Radioactivity Laboratory at

iThemba LABS 26

2-2 The picture shows the lead castle supported by a metallic frame surrounding the HPGe detector 27

xiii

2-3 The open top view showing the detector (A) and a Marinelli beaker on top of the

detector (B) 28

24 Schematic diagram illustrating the electronic setup used to acquire the HPGe data 29

2-5 Coaxial Ge Detector Cross Section 30

2-6 A diagram showing a typical semiconducter with band gap Eg 30

2-7 A typical germanium detector cryostat and liquid nitrogen reservoir (dewar) 31

2-8 Basic architecture of an MCA 33

2-9 The energy calibration spectrum showing the lines (labelled) used to perform energy

calibrations a mixture of 40K 232Th and 238U was used as a source 36

2-10 Energy calibration of the spiked material points and the line of best fit 37

2-11 A Full Width at Half Maximum calibration graph with a line of best fit 39

2-12 A spectrum of 60Co for peak-to-Compton ratio determination 40

2-13 Photo of Marinelli beaker and the design of its geometry the bottom part shows its re-

entrant hole 42

3-1 A graphical representation of the region of interest window set around the 40K peak 48

3-2 A typical representation of a sample spectrum number 6 (Kloof sample) with

superimposed background spectrum on a log scale

3-3 The flow chart showing the steps followed in constructing the absolute efficien

curve

xiv

49

cy

51

3-4 The spectrum of Kloof sand sample showing the lines used during detection efficiency

calibration 53

3-5 Fit of relative efficiency (with parameters a amp b generated) as determined from lines

associated with the decay of 238U (for a Kloof sample number 6) 54

3-6 Fit of relative efficiency with parameters a amp b generated (for Kloof sample) as

determined from lines associated with the decay of 232Th 57

3-7 A fit of relative efficiency data with parameters a amp b generated as determined from

lines associated with 238U and 232Th decay (Kloof sample) 58

3-8 A relative efficiency curve for the sample number 6 (Kloof sample) 58

3-9 A typical absolute efficiency versus energy graph for various selected lines associated

with nuclides 238U 40K and 232Th from sample number 6 (Kloof sample) 59


lines associated with 238U and 232Th decay (Westonaria sand sample) 60

311 A fit of relative efficiency data with parameters a amp b generated as determined from

lines associated with 238U and 232Th decay (West coast sand sample) 60


lines associated with 238U and 232Th decay (Brick clay) 61


lines associated with 238U and 232Th decay (thorium + stearic sample) 61

3-14 The contents of channels of the measured spectrum S redistributed to the re-binned

spectrum S 65

xv

3-15 Flow chart showing how a standard spectrum was obtained 66

3-16 The background subtracted re-binned standard spectra for uranium 67

3-17 The background subtracted re-binned standard spectra for thorium 68

3-18 The background subtracted re-binned standard spectra for potassium 69

3-19 Reduced chi-square (measure of the goodness of fit) for FSA fit of Westonaria

sample as a function of lower cut-off energy 73

3-20 The background subtracted Kloof (a )and West Coast(b) sample spectra and their fit for

a long measurement (below the 300 keV energy) 74

3-21 The background subtracted Brick clay (c) and thorium sample(d) spectra and their fit for


322 The background subtracted Kloof sample spectrum for a long measurement and

the fit (for energies between 300 and 1000 keV) 76

3-23 The background subtracted Kloof sample spectrum for a long measurement and the

fit (for energies between 1000 and 2000 keV) 77





xvi

3-26 The background subtracted Kloof sample spectrum for a short measurement and the


3-27 The background subtracted Kloof sample spectrum for a short measurement and


3-28 The background subtracted thorium + stearic acid sample spectrum and the fit for a

long measurement (for energies between 300 and 1000 keV) 82





3-31 A typical 609 keV peak due to 214Bi (for Kloof sample number 6) with a fit 85

3-32 A typical 583 keV peak due to 208Tl ( for thorium + stearic acid sample number 5) with

a fit 85

4-1 The comparison of the three nuclides for Westonaria sand (long measurement) in both

window and FSA analyses 101

4-2 The comparison of the three nuclides for Westonaria sand (short measurement) in

both window and FSA analyses 101

4-3 The percentage uncertainties for activity concentrations as a function of nuclide for

Westonaria sand sample 101

xvii

4-4 The comparison of the three nuclides for Kloof sand (long measurement) in both


4-5 The comparison of the three nuclides for Kloof sand (short measurement) in both



Kloof sand sample 102

4-7 The comparison of the three nuclides for West Coast sand (long measurement) in both


4-8 The comparison of the three nuclides for West Coast sand (short measurement) in both


4-9 The percentage uncertainties for activity concentrations as a function of nuclide for West

Coast sand sample 103

4-10 The comparison of the three nuclides for Brick clay (long measurement) in both


4-11 The comparison of the three nuclides for Brick clay sand (short measurement) in both



Brick clay sample 104

4-13 A graph showing correlation of activity concentration determined using the WAM vs

FSA (on average the two methods agree well within the correlation coefficient of

0932) 105

xviii

4-14 The activity concentration ratios (WAFSA) of uranium thorium and potassium long

measurement for various samples 106

4-15 The activity concentration ratios (WAFSA) of uranium thorium and potassium short


4-16 Activity concentration of nuclides for the high thorium content sample 109

4-17 Calculated transmission factors at different matrices for a 1000 cm3 Marinelli as a

function of γ-ray energy 113

4-18 The transmission factor for a 500 cm3 Marinelli at different densities with an increase in

energy 114

4-19 The volume effect on the transmission factor for different fillings (with sand of density

16 gcm3 ) of Marinelli as a function of energy 115

4-20 The differences in the transmission factors of (Westonaria sand) with regard to full and

half full Marinelli beaker as a function of energy 117

4-21 A filled Marinelli beaker showing an incoming photon and possibilities of interaction

in both the beaker and detector 118

C-1 The background spectrum of Marinelli beaker full of tap water 127

D-1 The Marinelli beaker with a spherical model at the center 128

xix

C h a p t e r 1

1 Introduction

In 1895 the German physicist Wilhelm Roentgen identified penetrating radiation which

produced fluorescence1 and which he named X-rays In 1896 two months later Henri

Becquerel discovered that penetrating radiation later classified as α β and γ rays were

given off in the radioactive decay of uranium and thus opened a new field of study of

radioactive substances and radiations they emit [Sha72]

Rutherford and Soddy were the first to suggest that radioactive atoms disintegrate into lighter

structures as they emit radiation This suggestion received powerful support with the discovery

that the α-particle was just an ionised atom of the element helium Many of the newly

discovered elements were found in various fractions of uranium ores and this the heaviest

naturally occurring element was soon suspected to be the parent substance [Ral72] It is

presently known that uranium consists naturally of a mixture of 238U (9927) 235U (072)

and 234U (0006) thorium and potassium were also identified as the radioactive parents with

some decay products Refer to Figures 11 12 and 13 for the decay processes of natural

radionuclides 238U 232Th and 40K into their daughter nuclei

Soils are naturally radioactive primarily because of their mineral content The main

radionuclides are 238U 232Th and their decay products and 40K The radioactivity varies from

one soil type to the other depending on the mineral makeup and composition [Dra03] The

objective in the measurement of the radioactivity in soil is to asses the radionuclide

concentrations and these concentrations may be used to characterise substances and relate the

1The emission of electromagnetic radiation especially of visible light stimulated in a substance by the absorption of incident radiation and persisting only as long as the stimulating radiation is continued

1

radiometric properties to physical properties of the material This may be of use in mineral

separation for example

11 The atomic nuclei and radioactivity an overview

This section describes the nature of atoms their building blocks and the nature of the forces

playing a role in it In the fourth century BC the Greek philosopher Democritus believed that

each kind of material could be subdivided into smaller and smaller bits until the limit beyond

which no further division was possible These building blocks of matter invisible to the naked

eye were referred to as atoms This speculation was confirmed by experimental scientists

(Dalton Avagadro Faraday) over 2000 years later Once the classification and kind of atoms

have been studied according to the rules governing their combination in matter by the

chemists the next step was to study the fundamental properties of an atom of various

elements This kind of atomic physics led to the discovery of radioactivity of certain species of

atoms [Kra88] Rutherford then used these radiations of atoms as probes of the atoms

themselves In 1911 he then proposed the existence of the atomic nucleus which was

experimentally confirmed by Geiger and Marsden A new branch of science which is now

called nuclear physics was then born This branch of physics is dedicated to studying matter at

its fundamental level

A nucleus X is made up of Z protons and N neutrons (nucleons) with the notation

with atomic mass number A = Z + N where X is a nuclide symbol The mass of a nucleus is

less than the sum of the individual masses of the protons and neutrons which constitute it

The difference is a measure of the nuclear binding energy which holds the nucleus together

This is the energy required to break it into separate neutrons and protons If the nuclear radius

is R then the corresponding volume (43)πR

NAZ X

3 is found to be proportional to A This

relationship is expressed in inverse form as

R = R0A13 (11)

2

with the value of R0 asymp 12 x 10-15m

The description of the nucleus can be understood with the aid of different models Two of

these are the liquid drop model and the shell model [Bei87 Eva55]

111 Radioactive Decay

Protons are positively charged and repel one another electrically Therefore an excess of

neutrons which produce only an attractive force is required for stability thus leading to N gt Z

for stable nuclei There is a limit to the ability of neutrons to prevent the disruption of the

nucleus by the Coulomb repulsion This phenomenon therefore leads to instability of nuclei

The instability can also be attributed to the unstable configurations due to the filling of

quantum states by the nucleon [Hew85]

112 Decay modes

Because of their instability nuclei decay by α β or γ emissions Many naturally occurring

heavy nuclei with 82 lt Z le 92 decay by α emission in which the parent nucleus loses both

mass and charge (A Z) [Ral72] The α (4He-nucleus) type reaction can be represented as

(12) γα ++rarr minusminus

42

42YX A

ZAZ

where X represents a chemical symbol of the parent atom and Y that of the daughter In some

emissions there is no γ emission

In β- particle emission a neutron (in the nucleus) is converted into a proton electron and an

anti-neutrino

epn νβ ++rarr minus01

11

10 (13)

3

Although free electrons do not exist inside the nucleus a β particle originates there and must

pass the nuclear potential barrier to escape [Ral92] This leads to the equation

eA

ZAZ YX νγβ +++rarr minus+

011 (14)

As in the α particle case the atomic mass number and atomic number are conserved The γ

term allows for the possibility that a daughter nucleus will be formed in an excited state while

some transitions go directly to the ground state The β- particle emission is an example of the

radioactive decay of a nuclide with neutron excess In this case a neutron is converted to a

proton according to equation (13)

The neutron-deficient nuclei emit a positron as they go to stability by

(15) enp νβ ++rarr +01

10

11

and the transformation is now

(16) eA

ZAZ YX νγβ +++rarr +

minus011

The energy of α and γ- radiation is discrete and well defined whilst β emission gives βs with a

continuous spectrum due to the varying amount of energy taken away by the neutrino

In the case of electron capture (EC) the neutron-deficient nuclei must decay by a p rarr n

conversion but have daughter products whose mass is greater than the maximum acceptable

for positron emission Therefore these nuclei can only decay by the capture of one of the

orbital electrons The atomic number is then reduced by one unit due to the negative charge

acquired by the nucleus and thus yielding the same daughter that would have been produced

by the positron emission Figure 11 in section 131 presents the decay scheme of 40K in which

4

the electron capture (EC) is in competition with positron emission in addition to β- decay to 40Ca the decay to 40Ar has two competing modes of decay that is β+ and EC The electron

capture is represented by the type of reaction

(17) eA

ZAZ YeX νγ ++rarr+ minus

minusminus 1

01

113 Decay rates

The radioactive decay rate of a nucleus is measured in terms of the decay constant λ which is

the probability per unit time that a given nucleus will decay and this is related to its

half-life2 Each radioactive nucleus has its own characteristic half-life If there are N radioactive

nuclei in a sample the rate of decay will then be given by

NdtdN λminus= (18)

where the minus sign indicates that N is decreasing with time The solution of this equation is

(19) teNtN λminus= )0()(

with N(0) being the number of nuclei present at t = 0 The half-life t12 may be expressed in

terms of λ from equation (113) as

λ

2ln21 =t (110)

The activity A is defined as the number of decaying nuclei per unit time and it can be

represented by

2 The time needed for half of the radioactive nuclei of any given quantity to decay

5

NdtdNA λ=minusequiv (111)

The unit is the Becquerel (Bq) with the historical unit being the Curie (Ci) where 1 Ci = 37 x

1010 decays per second and 1 Bq = 1 decay per second In this study the results are given in

terms of activity concentrations which are expressed in units of Bqkg

12 Types of environmental radioactivity

Radioactivity on the earth can be categorized according to three different types namely those

of primordial cosmogenic and anthropogenic nature [Mer97]

bull Primordial radionuclides these have half-lives sufficiently long that they have

existed since the formation of the earth and from the radioactive decay of these

secondary radionuclides are produced (eg 40K 232Th and 238U)

bull Cosmogenic radionuclides primary radiation (protons and other heavier nuclei)

originating from outer space called cosmic rays continuously bombard stable atoms in

the atmosphere and create radionuclides (eg 22Na 7Be and 14C) When cosmic rays

strike the atmosphere they produce a nuclear cascade or a shower of secondary

particles Most of these are eventually stopped before they reach the surface of the

earth except for energetic muons (micro) and neutrons (n) which may penetrate all the

way into the earth

bull Anthropogenic radionuclides these are man-made radionuclides released into the

environment through for example the testing of nuclear weapons nuclear reactor

accidents (eg Chernobyl) and in the radio-isotope manufacturing industry (137Cs 90Sr

and 131I)

6

13 Review of primordial radioactivity

Some of primordial radionuclides that now exist are those that have half-lives comparable to

the age of the Earth (eg 238U 232Th and 40K) Naturally occurring radionuclides can be divided

into those that occur singly and those that are components of chains of radioactive decay

131 Decay series of natural radionuclides

In this study the focus is on gamma-ray emitting daughter nuclei in the decay series of 2238U

232Th and 40K The decay series of 238U and 232Th are characterised more or less by the initial

part dominated by alpha decay and a part dominated by gamma-ray emission This contributes

to the difficulty in the radioactive measurements [Hen01] During a series of radioactive

decays the original radioactive (parent) nucleus N1 decays to another radioactive (daughter)

nucleus until the end of the series where a stable nucleus is formed (206Pb in the case of 238U

series and 208Pb for 232Th) see Figures 12 and 13 The number of parent nuclei N1 decreases

according to the form

dN1 = -λ1N1dt (112)

as discussed in section 113 The number of daughter nuclei increases as a result of the decay

of the parent nuclei and decreases as a result of the decay of its own which leads to

dN2 = (λ1N1 -λ2N2)dt (113)

After a long time equilibrium is reached where the production and the decay rates in the series

are the same [Kra88] so that dN2 = 0 Therefore the activities of all the radionuclides in the

chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7

and this phenomenon is referred to as secular equilibrium This is usually a very accurate

assumption except when daughter nuclei escape for example when the radioactive gas 222Rn

escapes in the decay series of 238U

Sir Humphry Davy discovered the potassium element in 1807 The element is the seventh

most abundant and makes up about 24 by weight of the earths crust Ordinary potassium is

composed of three isotopes one of which is 40K (00118) a radioactive isotope with a half-

life of 128 x 109 years [www01] see Figure 11

t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-

Figure 11 40K decays by

The above figure shows tw

while on the other hand th

this nuclide is 128 x 109 yea

β+

0001

β+ and electron capture to 40Ar and by β- to 40Ca

o competing decay modes (β+-decay and EC) to the stable 40Ar

ere is 89 chance of decaying by β- to 40Ca The half-life (t12) for

rs

8

uranium (U) 92 25 X105 y

45x109

y

117 m

protactinium (Pa) 91

245 d 75x 104y thorium (Th) 90

actinium (Ac) 89

1600 y radium Ra) 88

francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85

140 d 310 m164micros

polonium (Po) 84

50 d 197 m bismuth (Bi) 83

stable 22 y 268 m lead (Pb) 82

3 05 m 132 m thallium (Tl) 81

206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny

Figure 12 A Z-A Plot indicating how the 238U nucleus decays the half-lives for the respective nuclides are indicated

9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny

Figure 13 A Z-A Plot indicating how the 232Th nucleus decays the half-lives for the respective nuclides are indicated

10

Most of the radioactivity associated with uranium in nature is due to its progeny that are left

behind in mining and milling The gamma radiation detected by exploration geologists looking

for uranium actually comes from associated elements such as radium (226Ra) and bismuth

(214Bi) which over time have resulted from the radioactive decay of uranium Uranium

constitutes about 2 parts per million (ppm3) of the Earths crust [www02] See Figure 12 for

the decay process associated with this nuclide

In the decay series of for example 238U the parent nucleus 226Ra decays to the daughter 222Rn

by an α decay and 222Rn decays further to 218Po and consequently to 214Pb Since 222Rn is a gas

it might escape the matrix and thus disturbing the secular equilibrium In this event the

activities of the 222Rn progeny will not be the same as their parents and this is an indication of

a disturbance of the secular equilibrium Therefore to obtain secular equilibrium samples are

generally sealed for the radon not to escape This implies that the activity concentrations are

the same for all members of the decay chain When secular equilibrium is reached in the decay

of 238U or 232Th it means that the activity concentrations of these nuclei can be determined by

measuring activity concentration of their γ-emitting progeny The disturbance of secular

equilibrium due to 220Ra (thoron) is less significant due to its short half-life that is 556 seconds

implying that the thoron build up will be negligible

232Th is a naturally occurring radioactive element discovered in 1828 by the Swedish chemist

Jons Jakob Berzelius It is found in small amounts in most rocks and soils where it is about

three times more abundant than uranium Soil commonly contains an average of around 6

parts per million (ppm) of this nuclide The main pathways of exposure are ingestion and

inhalation It was found to be present in the highest concentrations in the pulmonary lymph

nodes and lungs indicating that the principal source of human exposure is inhalation of

suspended soil particles [www02] Figure13 shows the decay process of this nuclide

3 1 ppm U =1225 Bqkg 238U 1ppm Th = 410 Bqkg 232Th 1000ppm = 302 Bqkg 40K [Mer97]

11

14 Literature review natural radionuclide activity concentration in soil

Soil consists of mineral and organic matter water and air arranged in a complicated

physiochemical system that provides the mechanical foothold for plants in addition to

supplying their nutritive requirements [Mer97] The inorganic portion of the surface soils may

fall into a number of textural classes depending on the percentage of sand silt and clay Sand

consists largely of primary minerals such as quartz and has particle size ranging from 60 microm to

about 2 mm Silt consists of particles in the range of 2 to 60 microm while clay particles are

smaller than 2 microm in diameter [Van02a]

The Table 11 shows the values of natural radioactivity in typical soil of volume 1 km times 1 km

and 1 m deep The soil density was assumed to be 16 gcm-3

Nuclide Typical crustal activity concentration (Bqkg)

Mass in 106 m3 Activity in106 m3

238U 25 2800 kg 40 GBq 232Th 40 15200 kg 65 GBq 40K 400 2500 kg 630 GBq 226Ra 48 22 g 80 GBq 222Rn 10 14 microg 95 GBq

Table 11 Amount of naturally occurring radionuclides in typical soil of a volume 1 km times 1 km and 1 m deep [Van02b]

Substantial amounts of radionuclides are found in the earths crust In fact the natural

radioactivity is largely responsible for the fact that the interior of the earth is hot and molten

[Van02b]

The term radiometric fingerprinting describes the identification of mineral species based on

the difference in radionuclide concentrations [Dem97] In soil measurements a correlation

between activity concentrations and grain size has been determined in previous studies While

12

40K activity concentration varies slightly with grain size 238U and 232Th concentrations increased

with an increase in grain size [Van02a] For example Table 12 presents results found in one

case of the difference in activity concentrations for 238U and 232Th which are used to

fingerprint the sediments See also Table 13 for an example of radionuclide fingerprinting with

regard to different minerals

Sediment type 238U-series (Bqkg) 232Th-series (Bqkg)

Sand (gt 63microm) 93 plusmn 09 97 plusmn 09

Mud(lt 63 microm) 462 plusmn 19 456 plusmn 19

Table 12 Characteristic radiometric fingerprints of sand and mud The values are derived from 238U and 232Th activity concentrations of untreated total samples [Van02a]

141 Methods used to determine activity concentrations in soil

There are different methods used in the measurements of activity concentrations in soil These

include laboratory-based measurements using γ-ray methods of analysis and in-situ type of

measurements Examples of these methods will be briefly described in section 143 The focus

in this study is on γ-ray measurements in the laboratory which is based on the principle of

interaction of γ-rays with matter a subject to be discussed in the next section These

interactions need to be well understood in order to clarify results obtained in Chapter 4

13

142 Interaction of gamma rays with matter

There are three primary processes by which γ-rays interact with matter These are photoelectric

absorption Compton scattering and pair production

1421 Photoelectric absorption

Photoelectric absorption takes place when there is an interaction of a γ-ray photon with one of

the bound electrons in an atom as shown in Figure 14 All the energy of the photon is

transferred to the electron The electron is ejected from its shell with a kinetic energy Ee given

by

be EEE minus= γ (115)

where Eγ is the gamma ray energy and Ee the binding energy of the electron in a shell The

atom is left in an excited state with an excess of energy Eb and recovers its equilibrium by de-

exciting and thus redistributing its energy between the remaining electrons in the atom This

may result in the release of further electrons from the atom a process called Auger cascade

[Gil95] A vacancy left by the ejection of the photoelectron may be filled by a higher energy

electron falling into it with the emission of characteristic X-rays (as in Figure 15)

γ-ray

Ee

Eγ Nucleus

Electron Figure 14 A schematic representation of the mechanism of photoelectric absorption where a γ-ray with energy Eγ interacts with a bound electron

14

Nucleus

Kα X-ray

γ-ray Electron

Figure 15 The diagrammatic representation of emission of fluorescent X-rays The cross-section for photoelectric absorption is dependent on the atomic number Z This

varies somewhat depending on the energy of the photon At MeV energies this dependence

goes as Z to the 4th or 5th power The lower the photon energy and the higher the Z of the

material in which this photon interacts the higher the probability of absorption and this

becomes an important consideration when it comes to choosing γ-ray detectors [Leo87]

1422 Compton Scattering

The incident γ-ray interacts with an electron of an absorbing material Part of the γ-ray

energy is then transferred to this electron The energy imparted to the recoil electron is

given by

γγ EEEe minus= (116)

where Eγ is the energy of the incoming photon with E΄γ being the energy of the deflected

photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)

where m0 is the mass of an electron and c is the speed of light The incoming γ-ray is then

deflected through an angle θ with respect to its original direction Putting different values of θ

into this equation provides a response function with energy Thus with θ =0deg that is scattering

directly forward from the interaction point Ee is found to be 0 and no energy is transferred to

the electron At the other extreme when the gamma ray is backscattered and θ =180deg the term

within curly brackets is still less than 1 so only a proportion of the gamma-ray energy will be

transferred to the recoil electron which gives rise to the Compton edge This corresponds to

maximum energy transferred to recoil electron At intermediate scattering angles the amount

of energy transferred to the electron must be between those two extremes [Gil95] Figure 16

shows Compton scattering

Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ

Figure 16 The diagrammatic illustration of the mechanism of Compton scattering

16

1423 Pair Production

This process as shown on the diagram in Figure 17 is energetically possible if the γ-ray energy

exceeds twice the rest mass of an electron that is 102 MeV The entire energy is converted in

the field of an atom into an electron-positron pair The pair production cross-section does not

become significant until Eγ exceeds several MeV The positron is an anti-electron and after it

slows down and almost comes to rest it will be attracted to an ordinary electron Annihilation

then takes place in which the electron and positron rest masses are converted into two γ-rays

each with energy of 0511 MeV These annihilation γ -rays are emitted in opposite directions to

conserve momentum and they may in turn interact with the absorbing medium by either

photoelectric absorption or Compton scattering [Lil01]

In this study the focus is on γ-rays of energies less than 3 MeV thus pair production does not

play a major role The cross sections for this process are higher at energies above 3 MeV as is

confirmed in Figure 18

posit

electronIncident γ-ray

elect511 keV

Figure 17 The diagrammatic illustra

E

Eγ

ron

ron 511 keV

tion of pair production

17

1424 Attenuation Coefficients

The attenuation coefficient is defined as a measure of the reduction in the gamma-ray intensity

at a particular energy caused by an absorber [Gil95] Photoelectric interactions are dominant at

low energy Compton scattering at mid-energy ranges while pair production is dominant at

high energies In the low-energy region discontinuities in the photoelectric curve appear at

gamma-ray energies which correspond to the binding energies of electrons in the various

shells of the absorber atom The edge lying highest in energy corresponds to the K shell

electron For gamma-ray energies slightly above the edge the photon energy is just sufficient

to undergo a photoelectric interaction in which the K electron is ejected from the atom For

gamma rays below the edge this process is no longer energetically possible and therefore the

interaction probability drops abruptly Similar absorption edges occur at lower energies for the

L M electron shells of the atom [Kno79]

The total cross section σtot for the photon atom interaction may be written as

cpppetot σσσσ ++= (118)

where σpe σpp and σc are respectively the cross-sections for photoelectric absorption pair

production and Compton scattering [Cre87]

Present tabulations of the mass attenuation coefficient microρ rely on theoretical values for the

total cross section per atom which is related to microρ according to

)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)

u (= 167 x 10-24 g) is the atomic mass unit and A is the relative atomic mass of the

target element

18

Figure 18 The linear attenuation coefficient of germanium and its component parts on a log-log scale [Gil95]

On multiplying the mass attenuation coefficient microρ by the density ρ of the material the result

will be the linear attenuation coefficient micro This phenomenon is an important part of this

study and will therefore be discussed in more detail in the Appendix D under the discussion

on self-absorption effects

143 Examples of gamma-ray spectrometry systems

bull In-situ

The successful demonstration of the in-situ γ-ray spectroscopy for the rapid and accurate

assessment of radionuclides in the environment has been witnessed over time This allows for

the measurement of γ-ray intensities in the soil without any soil sampling and treatment

Although soil sampling and subsequent laboratory analysis is still needed for confirmation of

results the number of samples required can be reduced considerably

19

The accuracy of in-situ measurements in determining radionuclide activity concentrations in

soil relies on two primary elements the detector calibration and source geometry of the site

The field calibration can be expressed in terms of measured full absorption peak count rate N

(the subscript o represents the response at the normal incidence and the subscript f

represents the integrated response over all angles) the fluence rate Φ and the activity

concentration in the medium A [Mil94] The ratio of these quantities is then expressed as

A

NNN

AN O

O

ff Φbull

Φbull= (120)

where NfA is the total absorption peak count rate (cps) at some energy E for a particular

radionuclide per unit concentration of that radionuclide in soil NfNO is the angular

correction factor for radionuclide distribution in the soil NOΦ is the full energy peak count

rate to flux density for parallel beam of photons at energy E that is normal to the detector face

ΦA is the photon flux density from un-scattered photons arriving at the detector per unit

radionuclide activity for a given radionuclide distribution in the soil

The source geometry is evaluated as a volume source at a fixed height of one metre above the

ground The source geometry is primarily controlled by the depth profile of the radionuclide

being measured

A typical example of a field γ-ray measurement is a conventional portable coaxial HPGe

detector with a 12 relative efficiency and a resolution of 19 keV (relative to the 1332 keV for 60Co) A tripod supports the detector with the front part being 1 meter above the ground The

dewar has a capacity of 70 liters of liquid nitrogen (LN2) and holding time of five days The

detector is orientated in a downward facing way Detector calibrations for field γ-ray

spectrometry are performed by calculations and by using point like γ-ray sources [Fuumll99]

20

bull Laboratory based gamma ray spectroscopy

γ-radiation is a penetrating form of radiation and therefore can be used for non-destructive

measurements of samples of any form and geometry as long as standards of the same form are

available and are counted in the same geometry to calibrate the detector Various detector

types are used to measure γ-rays The one used in this study is the HPGe which has the

advantage of high-energy resolution

Most γ-ray spectrometry systems are calibrated with commercially mixed standards ideally the

matrix and geometric form of standards needs to match that of sample as closely as possible

However this is often difficult because one does not for example know the composition of the

sample to be analysed There is commercially available software for the analysis of the γ-ray

spectra Adjustments to the calibration for the corrections of density and effects such as self-

absorption need to be done This study utilises this method of analysis

15 The motivation for this study

The research interests in the Environmental Radiation Laboratory (ERL) at iThemba LABS

(South Africa) are as shown in the diagram below

Applied Radiometry

Environmental ApplicationsAgricultureMining explorations

Figure 19 Application of Radiometric methods in different fields

21

A connection between radiometry and minerals has been established and a method called

radiometric fingerprinting was the result [Dem98] In principle characterisation of samples is

based on the minerals percent composition of natural radionuclides such as 238U 232Th and 40K

by detection of the gamma rays from such minerals Samples are collected from the area of

surveillance and brought to the laboratory for analysis

Table 13 shows the results of a study on radiometric fingerprint of minerals associated with

heavy minerals deposits conducted in South Africa [Dem98]

Mineral 40K 214Bi 232Th

Quartz 116 (8) 2 (2) lt 9

Siltclay minerals 218 (10) 494 (11) 127 (3)

Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)

Table 13 Radiometric fingerprint given as activity concentrations (Bqkg-1) associated with heavy minerals in South Africa [Dem98] Uncertainties are given in brackets

22

The table shows that the values of natural radioactivity concentrations can be used to

characterise minerals according to grain size and composition

The Environmental Radioactivity Laboratory (ERL) has embarked on measurement of natural

and anthropogenic radionuclides in soil and liquid samples For this purpose a high purity

germanium detector (HPGe) housed in a lead castle is being used for laboratory-based

measurements while a MEDUSA (Multi Element Detector System for Underwater Sediment

Activity) scintillation-based detector is being used for in-situ measurements [Hen01] This

study will discuss a new method called the Full Spectrum Analysis (FSA) method in addition to

the conventional Window Analysis (WA) method to measure activity concentrations in soil

samples (see the next section) in the laboratory

16 The aim and scope of this study

Traditionally activity concentrations in soil samples are determined using what is called a

Windows Analysis (WA) procedure This involves analysing the spectrum measured (normally

in the laboratory) using windows or regions of interest (ROI) set around prominent γ-ray

peaks associated with the decay of 238U 232Th and 40K The windows are used to determine the

net counts (that is after an appropriate background subtraction) in the peak of interest By

using these counts with the branching ratio (associated with a particular γ-decay path)

measurement live time sample mass and full energy peak detection efficiency it is possible to

calculate the activity concentrations

A new technique for measuring primordial radionuclide activity concentration in soil samples

with HPGe is introduced in this study This technique called Full Spectrum Analysis (FSA)

uses the full spectral shape and standard spectra to calculate the activity concentrations of

238U 232Th and 40K present in a geological matrix [Hen01]

The FSA technique was first used in conjunction with the MEDUSA detector by the KVI

Nuclear Geophysics Division [Hen01] The MEDUSA detector which detects γ-radiation by

23

means of a scintillator (BGO or CsI) is used to perform in-situ measurements of natural

activity concentrations on seabeds [Ven00] and on land [Hen01]

FSA involves the fitting of a measured γ-ray spectrum (~200 keV to 3 MeV) by means of a

linear combination of the three so-called standard spectra and a background spectrum Each

standard spectrum corresponds to the response of the detector in a particular geometry

(normally that of a flat bed) for a sample containing 1 Bqkg of a particular nuclide (238U 232Th

and 40K) These standard spectra are normally obtained via measurement or by means of

Monte Carlo simulations The measured spectrum S is considered to be a superposition of

weighted standard spectra where the factors Ck CU and CTh are the activity concentrations of

each nuclide in the sample [Dem97] Mathematically it can be expressed as

)()()()()( iSiSCiSCiSCiS BThThUUKK +++= (121)

The spectrum deconvolution was applied and the coefficients CK CU and CTh were determined

using the χ2 minimisation technique

In this study the results from FSA and WA of HPGe spectra of a variety of sediment samples

are critically compared after which the advantages and disadvantages of each method are

established

17 Thesis outline

The next chapter will talk about the experimental techniques The HPGe detector system used

will be described in detail in chapter 2 while associated experimental work and data analysis

are discussed in chapter 3 The results will be presented and discussed in chapter 4 Finally a

summary and conclusion will be given in chapter 5

24

Chapter 2

Experimental Methods

Various types of detector differ in their operating characteristics but all are based on the same

fundamental principle the transfer of part or all the radiation energy to the detector mass

where it is converted into an electrical pulse The form in which the converted energy appears

depends on the detector and its design [Leo87] In this study a high purity germanium (HPGe)

detector is used The operation of this detector involves the following first the photon energy

is completely or partly converted into kinetic energy of electrons (and positrons) by

photoelectric absorption Compton scattering or pair production second the production of

electron-hole pairs third the collection and measurement of charge carriers

The various components of the HPGe detector used will be discussed in this chapter The

process followed in executing measurements will also be described The performance

characteristics of the detector will also be presented

21 The HPGe gamma-ray detection facility

The facility is used to measure natural and anthropogenic activity concentrations in soil and

liquid samples (though in this study the focus is on soil samples) The gamma ray

spectroscopy is mainly used for the analysis of natural gamma rays from potassium and the

progenies of uranium and thorium It can also be used to measure artificial radioactivity such

as the activities from cesium strontium etc The available equipment in the laboratory

includes an HPGe detector lead (Pb) shielding Marinelli beakers (for sample holding) PC-

based data acquisition system digital weighing balance and standards

25

211 Physical layout

Figure 21 shows experimental set up used in the present study (the picture was taken in the

Environmental Radiation Laboratory (ERL))

Lead Castle (detector inside) Amplifier

NIM crate

Dewar MCA card inside Oscilloscope DesktopHose (LN2

filling)

Figure 21 The picture showing the setup of the Environmental Radioactivity Laboratory at iThemba LABS

The lead castle which opens from the top shields the detector and the dewar underneath is

for holding liquid nitrogen (LN2) The oscilloscope is used to set and monitor the pulse

properties while the NIM crate carries the amplifier After amplification the signal is processed

in the MCA card in the PC and then displayed to the desktop

All radioactive sources are kept in the storeroom far away from the set up (approximately 5

meters) in order to avoid the contribution of such sources to the background during counting

26

The laboratory has an air conditioning facility that ensures the maintenance of the normal

temperatures around 18 degC

bull Lead Castle

Lead is the material employed in the shielding of the detector used in this study It makes a

good shielding material due to its high density and large atomic number A standard 25

(relative efficiency) detector measurement in a 10 cm thick lead shield will reduce the

environmental background by a factor of 1000 thus enabling one to measure

301000 asymp times weaker sources with the same statistical accuracy [Ver92]

In this study a 10 cm thick lead castle was used The inside of the castle was lined with a

copper layer of 2 mm thickness The copper layer is there to attenuate the X-rays from the lead

(see the Figures 22 and 23) A typical background spectrum measured with the ERL HPGe is

shown in Appendix C

Figure 22 The picture shows the lead castle supported by a metallic frame surrounding the HPGe detector

27

The black hose shown in Figure 22 is for the filling of the detector dewar with liquid nitrogen

A B

Figure 23 The open top view showing the detector (A) and a Marinelli beaker on top of the detector (B)

212 HPGe technical specifications

The detector used is a closed end-coaxial Canberra p-type (model GC4520) with a relative

efficiency of 45 The germanium crystal is located inside the lead shield The vertical dipstick

cryostat (model 7500SL) which is cooled by liquid nitrogen is contained inside a dewar (see

Figure 27) The detector crystal has a diameter of 625 mm and a length of 595 mm

213 Electronics

The electronic system for this semiconductor detector (HPGe) is shown schematically in

Figure 24 The system consists of a detector bias supply (SILENA model 7716) preamplifier

(model 2002CSL) amplifier (model ORTEC 572) multi channel analyser (OXFord-Win) and

a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector

Figure 24 Schematic diagram illustrating the electronic setup used to acquire the HPGe

data

bull Detector

The detector is a cylinder of germanium with an n-type contact on the outer surface and the

p-type contact on the surface of an axial well see Figure 25 The n and p contacts are diffused

lithium and implanted boron respectively [USR98] The germanium detector like other

semiconducter detectors is a large reverse biased p-n junction diode The germanium has a net

impurity level of about 1010 atomscm3 so that with the moderate reverse bias the entire

volume between the electrodes is depleted and the electric field extends across this region

[USR98]

29

Figure 25 Coaxial Ge Detector Cross Section [USR98]

The radiation energy is transferred to the detector crystal by an interaction process (photo

electric interaction) which then creates electron-hole pairs

h+

Valence band

Conduction bande-

Eg

Figure 26 A diagram showing a typical semiconducter with band gap Eg

The mobile electrons in the conduction band were promoted under an influence of an electric

field from the valence band the holes in the valence band are also mobile but the mobility of

the latter is in the opposite direction to the former This movement of electron hole pairs (e-

h+) in a semiconducter constitutes a current If these arrive at their respective electrodes the

30

result is a current proportional to the energy deposited in the crystal or a pulse [Lil01] This is a

small signal requiring amplification

The energy required to create an electron-hole pair across the Ge band gap (Eg) is

approximately 3 eV thus an incident gamma ray with an energy of several hundred keV

produces a large number of such pairs leading to good resolution and low statistical

flactuations These are desireable properties of a detector HPGe detectors are operated at

temperatures of around 77 K in order to reduce noise from electrons which may be thermally

excited across the small band gap at standard temperatures [Lil01] There are weekly fillings of

the ERL HPGe liquid nitrogen dewar (capacity of about 20 liters) to provide for such low

temperatures

The following is a cross sectional diagram of a germanium detector with a dewar

Figure 27 A typical germanium detector cryostat and liquid nitrogen

reservoir(dewar)[Gil95]

31

bull Detector bias

Radiation detectors require the application of an external high voltage for their proper

operation This voltage is normally referred to as detector bias and the high voltage supplies

used for this task are often called detector-bias supplies [Leo87] The SILENA model 7716

detector bias supply was used in this study A bias voltage of approximately 35 kV was

supplied and as photon interaction takes place within the depleted region charge carriers are

swept by the electric field to their collecting electrodes The specified depletion voltage for the

HPGe used is in fact 3 kV

bull Preamplifiers

The main function of the preamplifier is to amplify the weak signal and send it through to the

cable that connects the preamps with the rest of the equipment The preamps are mounted as

close as possible to the detector to minimise the length of the cable since the input signal is

very small The longer the length of the cable the more the capacitance and that reduces the

signal-to-noise ratio [Leo87] Therefore the manufacturing of the built-in preamplifiers

minimises this effect Furthermore when the detector system is cooled the preamplifier also

indirectly gets cooled thus reducing the chances for thermal excitation of charge which could

bring about leakage current4 A charge sensitive preamplifier will convert the charge into a

voltage pulse proportional to the energy deposited in the detector crystal The preamplifier

used in this study is of the model 2002CSL

bull Amplifier

The amplifier (model ORTEC 572) then further amplifies the pulse from the preamplifier to a

bigger size The pulse needs to be shaped to a more convenient form therefore the amplifiers

4 The unwanted current leaking between two electrodes under voltage

32

frequency response is set by a shaping time constant τ which is 6 micros for the amplifier

[USR98] Should a second signal arrive within the given period τ it will ride on the tail of the

first and its amplitude will be increased The energy information will therefore be distorted

resulting in a phenomenon called pile-up which is when pulses are too close together to be

separated [Leo87] This is not a problem in this study since the detector system dead time was

always less 1 Pulse shaping can also be used to optimise the signal to noise ratio

bull Multi Channel Analyser (MCA)

The operation of the multi channel analyser is based on the principle of converting an analog

signal which is basically the pulse amplitude into an equivalent digital number usually referred

to as a channel After this is done the digital information will be stored in the memory to be

displayed on the monitor This activity is in principle carried out by the Analog to Digital

Converter (ADC) [Kno00] The pulses are collected sorted according to pulse height in the

ADC and a γ-ray spectrum is generated Therefore the performance of the MCA is primarily

dependent on the ADC The results discussed in this thesis were measured using an MCA card

(OXFord-Win) in a PC using the OXWIN software program The MCA diagram is shown

below

plotter printer disc Other output devices

Monitor

MemoryControl logicA D C

Figure 28 Basic architecture of a MCA

33

214 Figure of merit

To keep track of the performance and reliability of the detector it is imperative to keep on

checking our results based on the detector specifications This can be achieved by doing the

energy calibration checking the Full Width at Half Maximum (FWHM) and determining the

peak to Compton ratio The background measurements were done in each case to ensure

derivation of proper concentrations These concepts are discussed in this section

bull Energy calibration

Prior to acquisition of the data energy calibration has to be performed as part of the setting up

procedure Various techniques of determining the energy at a particular channel are

implemented as this is a requirement by most nuclear applications In some MCAs a simple

two-point energy calibration is used to determine both the offset and slope by the equation

BchAE += )( ( 21)

where E is the energy and ch is the channel number and A and B are constants thus the

energy as a function of channel number can be directly read out The MCA systems in use

allows the user to choose between first-order (linear) or second order (quadratic) equations

that use a least square fit to data points In this study a second order equation was used

because the detection and amplification are not always exactly linear and this can be written as

follows

(22) CchBchAE ++= )()( 2

34

Any source whose peaks are known can be used to do the energy calibration In our study

sources such as a mixed liquid source was used (152Eu 60Co and 137Cs mixture) 232Th and 238U

sources were also often used The following is a particular case in which a mixture of 40K 232Th

and 238U was used as a source The energies of prominent γ-ray lines are presented in Table 21

below

Decay series

Decaying nucleus Energy (keV) FWHM (keV)

238U 226Ra235U 1861 151 232Th 212Pb 2386 154 238U 214Pb 2951 157 232Th 228Ac 3384 160 238U 214Pb 3520 160 232Th 208Tl 5830 173 238U 214Bi 6093 174 232Th 212Pb 7273 181 232Th 228Ac 9112 191 238U 214Bi 11203 203 40K 40K 14608 221 238U 214Bi 17645 238 238U 214Bi 22041 262 232Th 208Tl 26144 285

Table 21 γ-ray energies with associated Full Width at Half Maxima (FWHM) for γ-ray lines associated with decay of 40K and the series of 238U 232Th the energies are taken from [EML97]

The objective here is to derive a relationship between peak position in the spectrum and the

corresponding gamma-ray energy The mixture of three sources with well-known energies was

made to ensure that the calibration covers the entire energy range over which the spectrometer

is to be used The data on energies were taken from [EML97]

Figure 29 shows the spectrum for the mixture of materials used

35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd

Figure 29 The energy calibration spectrum showing the lines (labelled) used to performcalibrations a mixture of 40K 232Th and 238U was used as a source

Energy keV

36

energ

y

The spectrum has to be measured for long enough in order to determine the peak properties

with sufficient accuracy for the peaks to be used for the calibration The calibration process

involves marking the peaks to be used and their true energy see section 31 for the region of

interest (ROI) discussion The set ROI is used by the Oxwin software to calculate amongst

others the peak centroid

The relationship between energy and channel number is shown in Figure 210

R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174

Figure 210 A typical fit to data points used to energy calibrate the HPGe detector

system The energies used are also given in Table 21

37

bull Energy resolution

The energy resolution of the HPGe detector system as a function of γ-ray energy was

calculated after the energy calibration The energy resolution of the detector (at a particular γ-

ray energy) is conventionally defined as the full width-to-half maximum (FWHM) of the peak

divided by the peak energy Therefore the energy resolution which is a dimensionless fraction

is conventionally expressed in percentages Small percentage resolution of a peak implies good

resolution [Kno79]

In principle one should be able to resolve peaks at two energies which are separated by more

than one value of the detector FWHM at that energy

In order to parameterize the dependence of FWHM on γ-ray energy the FWHM data for the

lines given in Table 21 were fitted using a linear function The fit to the data are shown in

Figure 211 The results for the FWHM calibration shown in the Table 21 were obtained

from the following equation

BAEFWHM += (23) where A and B are constants deduced by the OXWIN software program and E is the γ-ray

energy The graph in Figure 211 was then plotted from these results

38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409

Figure 211 A Full Width at Half Maximum calibration graph with a line of best fit

According to the specifications of the detector the resolution should be 2 keV for the 1332

keV line for 60Co On interpolation the value of 22 keV was found for this value in this work

implying a deviation by 9 from the specified value

bull Peak to Compton Ratio

The Peak-to-Compton ratio is an important quantity defined as the ratio of the counts in the

channel corresponding to the highest number of counts per channel in the photo-peak (photo-

peak centroid) to the counts in the typical channel of the Compton continuum This typical

channel is defined as the region of interest between 1040-1094 keV for a 60Co source [Kno00]

The Compton continuum results from the Compton scattering in which the gamma rays

entering the detector will not deposit their full energy on interaction with matter This partial

energy event appears in the spectrum as an event below the full energy peak in the Compton

continuum The Peak-to-Compton ratio ranges from 30 to 60 for coaxial germanium detectors

when using the 1332 keV line associated with the 60Co decay [Kno00]

39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI

Figure 212 A spectrum of 60Co for peak to Compton ratio determination

A region of interest ROI (10401096) keV was established along the Compton continuum

and then the ratio of the number of counts in the photo peak to the continuum was

determined The Table 22 shows the data required for such a measurement

A ROI C G

30394 511 87 44482

Table 22 A table of counts in the chosen region of interest with number of channels along

the 60Co Compton continuum and in the channel corresponding to the highest number of

counts in the full energy peak A = Number of counts in the channel corresponding to the

highest number of counts per channel in the full energy peak ROI = Counts per channel in

the region of interest C = Number of channels in the region of interest G = Gross counts in

the region of interest

Counts per channel in the region of interest ROI = G C = 511 = Gross counts divided by

the number of channels within the region Therefore peak to Compton ratio = AROI = 59 1

40

This value is very close to the one specified by the manufacturer which is 581 [USR98] The

higher the value the more efficient the detector is and thus the value should preferably be

high

22 Sample Selection Preparation and Measurement

The types of samples studied were mainly soil taken from mine dumps in particular from

Kloof mine in Westonaria south west of Johannesburg (RSA) and beach sand from the west

coast of South Africa The samples were packed in plastic bags from the areas of surveillance

and brought to the laboratory at iThemba LABS At the laboratory the soil samples were put

in an oven (Labotech) and set to 105ordmC to allow for drying overnight After drying the samples

were crushed and sieved with a mesh having a hole diameter of 2 mm in order to remove

organic materials stones and lumps The information about treatment of samples can be

obtained from the general guide [ISO03] The samples were weighed on a digital weighing

balance (Sartoslashrius model BP2100S) with a precision of plusmn 001g and after sealing with silicon

sealant in Marinelli beakers the samples were allowed to stand for several days (about 21 days)

for secular equilibrium to be reached The following is a table of sample information

Sample ID Mass(kg) Livetime (s) Volume (ml) (Estimated)

Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes

Thorium+stearic acid 5

067734 28740 1000 0677 Yes

Table 23 The table of the samples collected at different sites

41

bull Marinelli beaker

Environmental samples of low-level radioactivity are often measured in Marinelli beakers

specially designed to provide good detection sensitivity Full Energy Peak Efficiency (FEP)

variations are observed in this geometry for different sample types [Sim92] this is due to self-

attenuation effects a concept that is discussed later with results (see also Appendix D) See

Figure 213 and D1 for Marinelli beaker photo and a drawing of its dimensions respectively

Figure 213 Photo of Marinelli beaker and the design of its geometry The bottom part shows its re-entrant hole [Ame00]

In the Environmental Radiation Laboratory (ERL) at iThemba LABS the 1-liter Marinelli

beaker (Model VZ-1525) made of polypropylene material manufactured by Amersham

[Ame00] was used The precision with which the activity can be determined with this Marinelli

geometry is limited by the effect of self-absorption for which correction must be made

[Dry89] Self-absorptions effects were verified through the use of the Sima model [Sim92]

42

This was done on the basis of the difference in the samples density and volume in this study

The results for this will follow in chapter 4

In window analysis if the standard source has the same physical dimensions density chemical

composition and radionuclides present as in the sample the radioactivity of the sample is

simply determined by comparison of the count rates in the corresponding full energy peak of

the measured pulse height gamma ray spectrum [Par95]

23 Reference sources

The two reference sources IAEA-RGU-1 and IAEA-RGTh-1 prepared by the Canada Center

for Minerals and Energy Technology on behalf of the International Atomic Energy Agency

were used in this work [RL148] The ERL Laboratory at iThemba LABS bought the 40K (KCl

powder) reference

bull WA

The reference source used in this case was KCl of 99 purity this was used specifically for the

efficiency calibration The advantage of this standard source is the fact that it is easier to

handle and is not that hazardous The method of calibrating detector efficiency using this

standard is described in the next chapter The activity of this is given in the Table 24 below

This standard was also used in the FSA method of analysis

bull FSA

The information of the reference sources used in the FSA method of analysis is tabulated in

Table 24 The full details regarding the preparation of these are given by [RL148] except for

the 40K reference source in which KCl was used instead of K2SO4 as used by the IAEA

(reference manual [RL148] ) for example

43

Nuclide Used in which

method

Source Supplied in what form

Mass (kg)

Volume (ml)

Density (gcm3)

Activity Concentration

(Bqkg) 238U FSA IAEA (RGU) 04873 400 12 4940

232Th FSA IAEA (RGTh) 05157 400 13 3250

40K FSAWA KCl (99purity) 12721 1000 13 16258

Table 24 The table shows the data of reference materials used

The energy calibration was done independently for each source and the sample to be

measured It is seen in Table 24 that the volumes of the reference sources for uranium and

thorium differ significantly from those for the sample The effects of this on the results

presented below are discussed in chapter 4

24 Data acquisition

Each time a measurement is done energy calibration has to be done as part of the setting up

procedure before any data acquisition The counting time was preset on the Oxford-Oxwin

software used

Information regarding the spectra acquired with reference sources samples and background

(Marinelli filled with tap water) are given in Tables 25 and 26

44

Source type Measurement date

Elapsed Real time (s)

Elapsed Live time (s)

KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026

Table 25 Spectral information on reference sources (see Table 24 for information on Sources)

Long Measurement Short Measurement Sample

Code Elapsed

real time(s)

Elapsed live

time(s)

Elapsed real time(s)

Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594

Thorium+ stearic acid 5

28800 28740

Marinelli filled with tap water (Background)

116322 116312

Table 26 Spectral information on Samples and background (see Table 23 for more information on the samples)

45

Chapter 3

Data Analysis

In this chapter the two methods used in this work for determining the activity concentration

of 238U 232Th and 40K in sediments namely the Window Analysis (WA) and Full Spectrum

Analysis methods (FSA) are described

31 Window Analysis

In the Window Analysis method the activity concentrations A (Bqkg) in sediments are

calculated using the equation

)(EtiB

iN

LMrC

kgBqAε

prime= (31)

where is the net counts in the ith γ-ray peak associated with the nucleus of interest (primeiNC 238U

232Th or 40K) Lt is the live time associated with the sample spectrum M is the mass of the

sample εE the full energy peak detection efficiency at a particular energy E and rBi the

branching ratio of the energy line used (see Table 31 for branching ratios used in this study)

primeiNC is obtained from an analysis of the peak of interest using a region of interest (ROI) or

window set around the peak hence the term Window Analysis An example of a window set is

shown in Figure 31 where the 1461 keV line (40K) is focused on In this case the window starts

at an energy K (~1455 keV) and ends at an energy Q (~14665 keV) The region below line P

is due to the Compton continuum

In this study CNi was determined using the Oxwin MCA software The software calculates the

gross counts Cg in the window of interest (starting at channel s and ending at channel e)

according to the equation 32

46

(32) sum=

=

=ei

siig CC

where Ci is the counts in channel i The counts in the continuum are calculated using the

equation

(33) sum=

=

=ei

siCic CC

where CCi is the continuum counts in channel i

The software can therefore calculate the net counts CNi in a particular photopeak from

cgNi CCC minus= (34)

Even when a sample is not being counted by the HPGe counts are registered in the spectrum

due to room background (see Figure 32 for a sample and background spectra) The

contribution to CNi from room background has to therefore be subtracted A room

background spectrum was measured by using a Marinelli beaker filled with a 1 liter of tap

water This spectrum is shown in Appendix C The windows used in the analysis of the sample

spectra were used to determine Cbi the net background counts in the peaks of interest

The background subtracted net counts CNi in the ith peak was calculated using the expression

ibB

CiNiN C

LL

C

minus=primeC (35)

where LC and LB are the detector live times during the measurement of sample and room

background respectively

47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum

Figure 31 A graphical representation of the region of interest with window setting around the 40K peak

As can be seen from equation 31 the full-energy peak (also termed photo peak) detection

efficiency as a function of γ-ray energy is needed in order to calculate activity concentrations

and is discussed in the next section

48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6

Figure 32 A typical representation of sample (number 6b Kloof sample) spectrum with

superimposed background spectrum (measured using a Marinelli filled with 1litre of water) on a log scale

311 Determination of γ-ray detection efficiency

The method for determining the efficiency curve used in this work involves two steps The

first step involves the measurement of the relative detection efficiency using 238U and 232Th

lines as observed in the sample spectrum measured after secular equilibrium is achieved The

second step entails placing the curve on an absolute scale by using the 1461 keV (40K) line This

is done by calculating the absolute efficiency at 1461 keV for a Marinelli beaker filled to 1 litre

with KCl This is similar to the technique described in reference [Fel92]

49

One advantage of this approach is that the self-absorption effects are automatically taken into

consideration [Fel92] The other advantage is the fact that the KCl source is more convenient

in the sense that it is easier to handle from a safety point of view

It is assumed that the two decay chains are in secular equilibrium

The relative efficiency data were fit with a function of the form

b

EEa

=

0

ε (36)

where ε is the efficiency E is the γ-ray energy in keV (E0 = 1) with a and b being fit

parameters [Dry89]

On taking the logarithm of equation (36) one obtains

ln (37) 0

lnlnEEba +=ε

50

A flow-chart illustrating the steps used in more detail is given in Figure 33

1Calculation of relative

efficiencies

Curve fitting (ε = aEb)

2

Determination of Activity Concentration for KCl

Reference source 3

Determination of efficiencyat 1461 keV (using KCl)

4

Determination of the ratio

between 2 amp 4 5

Multiply the value in 5 by 2 6

Construction of absolute

efficiency

7

Figure 33 A flow chart showing the steps followed in constructing the absolute efficiency curve

51

The 238U and 232Th γ-ray lines used to construct the relative efficiency curves along with other

properties are given in Table 31 Generally the lines used have large branching ratios

However some lines such as the 609 keV and 583 keV lines associated with the decay of 214Bi

and 208Tl respectively were omitted since they are prone to coincidence summing [Gar01]

Furthermore lines overlapping with others were not used with the only exception being the

186 keV line (doublet due to lines 238U235U) and the 967 keV line due to 228Ac The γ-ray lines

from the radionuclide lines used in the efficiency calibration are shown on the Table 31 (and

Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series

226Ra 1861 005789 214Pb 2951 0185 214Pb 3520 0358 214Bi 7684 005 214Bi 9340 0032 214Bi 11203 015 214Bi 12381 0059 214Bi 13777 004 214Bi 17645 0159 214Bi 22041 005

232Th Series 228Ac 3384 0124 212Bi 7273 0067 228Ac 7948 0046 208Tl 8603 0043 228Ac 9112 029 228Ac 9668 0232

40K Series

40K 14608 01066

Table 31 The gamma ray lines used and their associated branching ratios the branching

ratios are taken from [EML97] branching ratio for 226Ra was corrected for the fact that it

is doublet with a 185 keV peak due to 235U

52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)

Figure 34 The spectrum of Kloof sand sample showing the lines used (see Table 31) duringdetection efficiency calibration

53

From the uranium series fit parameters (a and b) were determined using equation 37 These

parameters are used to determine the factor that is needed to join the thorium content to the

uranium content line using the equation 36 Calculations of the relative efficiencies for all the

lines including the 1461 keV were done and at this point the relative efficiency curve is

determined The fit parameters generated for a particular sample (Kloof sample) are presented

in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241

Figure 35 Fit of relative efficiency (with parameters a amp b) as determined from lines associated with the decay of 238U (for a Kloof sample number 6) Values were normalised relative to the 352 keV line

The Figures 36 and 37 depict the relative efficiency curve from thorium points and the curve

from a combination of both 238U and 232Th points respectively From the relative efficiency

curve in Figure 37 a normalization factor (step five from the flow chart in Figure 33) is

needed to multiply all the values corresponding to the points in Figure 38 to obtain the

absolute efficiency curve The absolute efficiency curve for this sample is shown in Figure 39

54

The KCl sample was used as a standard source and the absolute efficiency calibration was

determined using this sample The activity of 40K was calculated as follows

From equation (115) Nλ=Α

where A is the activity with λ as the decay constant and N the number of 40K nuclei in KCl In

order to obtain N one needs to find the number of moles in the KCl and therefore multiply

that with the Avagadros number NA = 6022 x 1023 This brings us to the number of moles n

as in the equation (38)

Mmn = (38)

with m as the mass of the KCl (1000 g) source and M the molar mass (74551 gmol)

Since (39) aNnN A timestimes=

with a being the abundance and that

21

2lnt

=λ from equation (114)

where t12 the half life for 40K is 1277 x 109y

Multiplying N by the activity constant λ and the abundance a of 40K in KCl which is equals to

117 x 10-4 gives the activity 16256 Bqkg

The KCl spectrum measured is shown in Figure 315 (section 321)

The absolute full-energy peak detection efficiency was then calculated using the expression in

equation 310

55

ALMr

C

tB 1461

1461 =ε (310)

where C1461 is the nett counts in the 1461 keV line (after background subtraction) and the

other symbols are as determined from equation 31 ε was found to be 000940 plusmn 000007 The

uncertainty quoted is that associated with counting statistics

This efficiency divided by the relative efficiency at 1461 keV yields a coefficient needed to

convert all the relative efficiencies to absolute efficiencies The absolute efficiency curve in

Figure 39 was generated using this procedure for the Kloof sample In the same manner

absolute efficiency curves were generated for the other samples The parameterisation of

absolute efficiencies (ε = a Eb) is given in each relative efficiency plot

56

The graphs of ln(Energy) versus ln(Relative efficiency) for other samples follow from Figures

310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572

Figure 36 Fit of relative efficiency with parameters a amp b generated (for a Kloof sample) asdetermined from lines associated with the decay of 232Th Values were normalized relative tothe 338 keV line

57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392

Figure 37 A fit of relative efficiency data with parameters a amp b generated as determined from lines associated with 238U and 232Th decay (Kloof sample number 6)

002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)

Figure 38 A relative efficiency curve for the sample number 6 (Kloof sample)

58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)

Figure 39 A typical absolute efficiencies versus energy graph for various selected lines associated with nuclides 238U 40K and 232Th for sample number 6b (Kloof sample)

59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)

Figure 310 A determined fromnumber 17A)

-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)

fit of relative efficiency data with parameters a amp b generated as lines associated with 238U and 232Th decay (Westonaria sand sample

U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)

fit of relative efficiency data with parameters a amp b generated as

lines associated with 238U and 232Th decay (West coast sand sample)

60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252

Figure 312 A fit of relative efficiency data with parameters a amp b generated as determined from lines associated with 238U and 232Th decay (Brick clay)

- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )

Figure 313 Adetermined from

a = 51057 b = -08147

2 4 6 8 1 0

ln(E)

fit of relative efficiency data with parameters a amp b generated as lines associated with 238U and 232Th decay (thorium + stearic sample)

61

312 Treatment of uncertainties in WA

The uncertainties contributing to the results in this method were propagated throughout by

adding them all in quadrature combinations An example of the uncertainty due to background

subtraction is as follows

from equation 35 it follows that

22 )()( ibiNibiNiN CCCC ∆+∆plusmnminus=C prime

where 22 )()( ibiNiN CCC ∆+∆=prime∆ (311)

prime∆ iNC is an uncertainty in the background subtracted net counts and are

uncertainties due to counting statistics for net and background counts

iNC∆ ibC∆

Now to get to the relative efficiency the background subtracted net counts will be divided by

the branching ratio (which also has its specified uncertainty from the manual [EML97]) This

now yields the following

b

iNrel r

C prime=ε (312)

Therefore the uncertainty in 312 will then be given by

22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62

The uncertainties from the live time and the sample mass were almost negligible and therefore

were treated as constants

Furthermore from equation 36

baE=ε

the relative uncertainties include the uncertainty in parameters a and b as follows

22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε

which is the uncertainty in the relative uncertainties (ignoring co-variances)

Although the uncertainties in a and b were determined these uncertainties were not

propagated in this study

The activity concentrations presented in chapter 4 by this method are calculated from

intensities of several γ-rays emitted by parent nucleus and therefore grouped together to

produce a weighted average activity per nuclide

These weighted average activity concentrations in the samples analysed (using the WA

method) are presented in Tables 41 to 49 in chapter 4

The equations in appendix A were used in the treatment of uncertainties for this method see

also the statistics of counting described in Appendix A2 to find out how weighted averages

are arrived at

63

32 Full Spectrum Analysis

The important aspects to consider in this method are the use of its full-spectral shape and the

so-called standard spectra in the calculation of the activity concentrations of natural

radionuclides 238U 232Th and 40K [Hen01] The total spectrum comprises a background

spectrum and the responses to the activity concentrations of the natural radionuclides These

responses are considered to be proportional to the activity concentrations and require detailed

knowledge of the standard spectra Each of the spectra corresponds to the response of the

detector in a particular geometry for a sample containing 1Bqkg of each nuclide [Hen03]

All the spectral features including the inclusion of the Compton continuum in the spectrum

makes this method a good one in the data analysis and this contributes to the reduction of the

statistical uncertainty in the data especially for relatively short measurements since in principle

more time is required for the accumulation of data with small uncertainties

321 Derived standard spectra

Energy calibration was done according to the calibration process already discussed in section

214 These energy calibrations were done independently for each standard spectrum

In general the relation between energy and channel number of the sample spectra measured

deviates from that of the standard spectra These deviations can be attributed for example to

temperature variations which consequently result in the varying in time of the relation

between energy and channel number [Kno79]

64

To take the differences in amplifications for samples taken at different times into account all

spectra were re-binned5 using the energy calibration parameters so that each spectrum has the

same channelenergy relationship chosen as 1 keV per channel for convenience

M(j)

j S S

Figure 314 The contents of channels of the measured spectrum S redistributed to the re-binned spectrum S

The channel i of the re-binned spectrum S can be mapped onto the channels j of the

measured spectrum S with a function i = M(j) and the contents of the channels of the

measured spectrums can then be redistributed over the channels of the re-binned spectrum S

[Sta97] A small FORTRAN program was developed to execute such a task see (appendix B)

The re-binning exercise is needed to try and correct for the small differences in the energy

calibration between the standard and sample spectra

The spectra were normalized by dividing each channel by the product of source mass live time

and activity concentration The flow chart in Figure 315 shows a summary of how standard

spectra were obtained

65

5 channels converted to equivalent energy values per bin

For a particular spectrum divide eachby a product of source mass livetime and activity concentration

Standard spectrum

Re-bin each spectrum such that 1 channel = 1 keV

Energy calibrate each spectrum

Measure reference spectrumsource on HPGe

Figure 315 Flow chart showing how a standard spectrum was obtained

Figures 316 317 and 318 show the re-binned spectra for the three standard sources used

which are those for the 238U 232Th and40K respectively

66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10

Figure 316 The background subtracted re-binned standard spectrum for uranium

Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)

Figure 317 The background subtracted re-binned standard spectrum for thorium

Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)

Figure 318 The background subtracted re-binned standard spectrum for potassium (Peaks labeled 1 2 3 and 4 are the full-energy peaks 438 keV due to second escape peak the annihilation peak (511 keV) the first escape peak (950 keV) and the 1461 keV due to 40K respectively

322 Chi-square minimization technique

Once the fixed relation between energy and channel number has been obtained the least-

square method is used to find the optimal activity concentrations using the Physica software

[Chu94] In this method the activity concentrations will follow from a fit of the calculated

standard spectrum to the measured one [Hen01] In the FSA the measured spectrum Y is

described as the sum of the standard spectra Xj multiplied by the activity concentrations Cj for

the individual radionuclides The background was subtracted from the individual spectrum in

each measurement before fitting

If a complex spectrum has to be decomposed into j known components the intensity Cj of

each component relative to that of its standard is determined by the requirement that

sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)

should be a minimum [Qui72Pre92Hen10] Y (i) and Xj(i) are counts in channel i recorded

under the same experimental conditions j represents the number of standard spectra used

with jmax= 3 since three standards sources (238U 232Th and 40K ) were used in this study i =

lec and n = hec are low energy and high energy cut-offs used during the minimization

procedure The factor n-m represents the number of degrees of freedom where n is the

number of data points and m the number of free parameters The choice of n-m assumes all

the channels to be independent [Hen03] The weight factor is given as the inverse of the

square of the standard deviation The standard deviations for each source were added in

quadrature combinations to the samples standard deviation

)(iw

The important part of equation 316 for FSA is in the definition of the weights w(i) and this

will be discussed next

70

Definition of weights

Let

AAA ii ∆=plusmnand

BB ii ∆=plusmnΒ

represent gross counts in the ith channel of the sample and background spectrum respectively

Now the real count rate obtained after background subtraction is given by

22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)

Were tA and tB are live times for the measured sample and background respectively The

uncertainty in the background-subtracted count rates is given by

22

∆+

∆=

B

i

A

ii t

BtA

σ (318)

The errors in (316) were added in quadrature combinations to give the total standard

deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71

where the subscripts S K Th and U are the sample potassium thorium and uranium spectra

respectively and with t being the live time associated with the spectra The background B was

subtracted from each spectrum that is in all three standard spectra plus the sample one

The weighting is then given by the inverse of the square of the standard deviations as follows

w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)

where Sσ is the standard deviation for the sample measurement

The minimization is such that

02

=partpart

jcχ ( for all j ) (322)

72

Several measurements on different samples were made with both methods and the Tables 23

and 26 show the information regarding such samples

The fit is reasonably good in general except for low energy cut-off energies less than about

300 keV This is due to the self-absorptions at lower energies as discussed later in chapter 4

The χ2reduced has been calculated for low energy cut-off energies ranging from 50 keV up to

300 keV (in steps of 50 keV) and with a high energy cut-off of 2650 keV These χ2reduced values

obtained are shown in Figure 319 for the different cut-off energies

0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e

Figure 319 Reduced chi-square (measure of the goodness of fit) for FSA fit of Westonaria sample as a function of lower energy cut-off (lec) (see equation 316)

73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)

Figure 320 The background subtracta long measurement (below 300 keV)

Energy (keV)

ed Kloof (a )and West Coast(b) sample spectra and their fit for

74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)

Figure 321 The background subtracted Brick clay (c) and thorium sample(d) spectra andtheir fit for a long measurement (below 300 keV )

75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)

Figure 322 The background subtracted Kloof sample spectrum for a long measurement and the fit (forenergies between 300 and 1000 keV)

76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500

Figure 325 The background subtracted Kloof sample spectrum for a short measurement and the fit(for energies between 50 and 500 keV)

79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000

Figure 327 The background subtracted Kloof sample spectrum for a short measurement and the fit (forenergies between 2000 and 2650 keV)

81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd

Figure 328 The background subtracted thorium + stearic acid sample spectrum and the fit for along measurement (for energies between 300 and 1000 keV)

82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd

Figure 330 The background subtracted thorium + stearic acid sample spectrum and the fitfor a long measurement (for energies between 2000 and 2600 keV)

The fit is not good for the energies ranging from 50 keV to about 300 keV as is witnessed

from Figures 320 b and 321c This is due to self-absorption effects a phenomenon to be

discussed in the next chapter

In order to see how good a fit is two energy lines from two samples of different densities were

chosen The Figure 331 shows how good the fit is at the 609 keV (214Bi line) for the Kloof

sample while Figure 332 shows the fit for the 583 keV (208Tl line) from the thorium + stearic

acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured

Figure 331 A typical 609 keV peak due to 214Bi (for Kloof sample number 6) with a fit

0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured

Figure 332 A typical 583 keV peak due to 208Tl (for thorium + stearic acid sample

number 5) with a fit

85

323 Treatment of uncertainties for FSA

The uncertainties in Cj from equation 316 were obtained using the Gauss-Newton method

This method proceeds by iterative means to calculate ∆C such that

CCC ∆+= 01 (323)

the aim of this method is to find a ∆C such that C1 is a better approximation to the best least

square fit solution [Chu94Pre92] If the method is repeated iteratively the series C1C2 C3

will converge until the sum of the squares of the differences between the data points and the

function being fitted is a minimum

To accomplish this the function f (xC) is expanded in a Taylors series about the point C = C0

and only the first order terms are kept [Chu94]

C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)

The equation above is an exact equality when f is linear in the parameters C that is all second-

order and higher derivatives are zero

The problem then is to minimize

2

00

11

2 )()(

part

∆partminusminus= sumsum

== CCCxf

Cxfyw kkk

N

kk

N

kkδ

for a system with M parameters this becomes

2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86

If the above expression is differentiated with respect to each of the unknowns ∆Cj and the

resulting expressions are set to zero the problem reduces to solving the matrix equation

rCA =∆ where A = (aij) r = (ri)

and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1

2δ is zero at the minimum provided the Gauss-Newton method is locally convergent

The advantage of this method is that linear least squares problems are solved in one iteration

An indication of the accuracy of the fit is displayed in the output of the Physica program as E1

and E2 where

iib=1Ε for i=1M (328)

where bii are the diagonal elements of B = A-1 the inverse of the matrix A B is called the

covariance matrix and E1 is referred to as the root mean square statistical error of estimate

The root mean square total error of estimate or standard error is displayed under E2 where

Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ

Therefore the accuracy of the parameters in a linear fit is

Ci plusmn E2i for j = 1M

87

Chapter 4

Results and Discussion

In this chapter the activity concentrations of 238U 232Th and 40K in the samples analysed as

derived from Windows Analysis and Full Spectrum Analysis are presented and compared

41 WA results

The activity concentrations and associated uncertainties as derived using long live time

measurements are given in Tables 41 - 45

Nuclide Energies (keV)


(Bqkg)

Full-energy peak

Absolute efficiency

Weighted Average Activity

Concentration (Bqkg)

238U series 226Ra238U 1861 3054 plusmn 50 00410214Pb 2951 3289 plusmn 29 00295214Pb 3520 3337 plusmn 27 00260214Bi 9340 2768 plusmn 102 00129214Bi 11203 2957 plusmn 35 00113214Bi 12381 2991 plusmn 65 00105214Bi 13777 3289 plusmn 83 000980214Bi 17655 3221 plusmn 38 000821214Bi 22041 3192 plusmn 63 000700

320 plusmn 5

232Th series 228Ac 3384 251 plusmn 15 00267212Bi 7273 193 plusmn 30 00154228Ac 7948 195 plusmn 51 00145208Tl 8603 264 plusmn 63 00137228Ac 9112 187 plusmn 09 00131228Ac 9668 228 plusmn 04 00126

21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940

Table 41 The activity concentration results for the Kloof sample number 6 (longmeasurement) by WA method

88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration

(Bqkg) 238U series 226Ra238U 1861 2821 plusmn 47 00451214Pb 2951 2520 plusmn 12 00318214Pb 3520 2691 plusmn 16 00278214Bi 9340 2359 plusmn 78 00132214Bi 11203 2519 plusmn 27 00115214Bi 12381 2552 plusmn 58 00107214Bi 13777 2992 plusmn 64 000983214Bi 17655 2752 plusmn 25 000815214Bi 22041 2822 plusmn 49 000687

263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940

Table 42 The activity concentration results for the Westonaria sample number 17A (long measurement) by WA method

89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940

Table 43 The activity concentration results for (long measurement) the West Coast sample number 3 by WA method

90


Activity Concentration (Bqkg)

Full-energy peak Absolute efficiency

Weighted Average Activity Concentration (Bqkg)

238U series 226Ra238U 1861 314 plusmn 29 0064 214Pb 2951 297 plusmn 20 00417 214Pb 3520 313 plusmn 21 00353 214Bi 9340 221 plusmn 65 00143 214Bi 11203 369 plusmn 32 00120 214Bi 12381 273 plusmn 49 00110 214Bi 13777 365 plusmn 58 000993 214Bi 17655 405 plusmn 37 000789 214Bi 22041 450 plusmn 64 000641

30 plusmn 14

232Th series 228Ac 3384 450 plusmn 30 00367 212Bi 7273 658 plusmn 53 00180 228Ac 7948 622 plusmn 58 00166 208Tl 8603 599 plusmn 64 00154 228Ac 9112 575 plusmn 43 00146 228Ac 9668 614 plusmn 47 00138

55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940

Table 44 The activity concentration results for (long measurement) the brick clay sample number 6 by WA method

91


Activitiy Concentration (Bqkg)



238U series 226Ra238U 1861 304 plusmn 79 00382 214Pb 2951 134 plusmn 23 00279 214Pb 3520 137 plusmn 17 00248 214Bi 9340 194 plusmn 135 00128 214Bi 11203 129 plusmn 27 00112 214Bi 12381 -09 plusmn -78 00105 214Bi 13777 -09 plusmn -117 000978 214Bi 17655 73 plusmn 149 000827 214Bi 22041 129 plusmn 27 000710

13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940

Table 45 The activity concentration results for (long measurement) the thorium + stearic acid sample number 5 by WA method

92

The activity concentrations and associated uncertainties as derived using short live time

measurements are given in Table 46 - 49

Nuclide Energies

(keV) Activity Concentration (Bqkg)




277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986

Table 46 The activity concentration results (short measurement) for the Kloof sample number6 by WA method

93





Concentrations (Bqkg)


257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940

Table 47 The activity concentration results for the Westonaria sample number 17A (short measurement) by WA method

94


Activitiy Concentration

(Bqkg)

Full-energy peak Absolute

efficiency



238U series 226Ra238U 1861 80 plusmn 27 00450214Pb 2951 42 plusmn 10 00317214Pb 3520 47 plusmn 07 00277214Bi 9340 75 plusmn 60 00132214Bi 11203 56 plusmn 14 00115214Bi 12381 -04 plusmn -62 00107214Bi 13777 -04 plusmn -69 000982214Bi 17655 67 plusmn 11 000814214Bi 22041 11 plusmn 51 000688

52 plusmn 05


46 plusmn 05

40K Series 40K 14608 54 plusmn 4 000940 Table 48 The activity concentration results for the West Coast sample number 3 (short measurement) by WA method

95

Nuclide Energies

(keV) Activitiy Concentration (Bqkg)




32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986

Table 49 The activity concentration results for the brick clay sample number 6 (short measurement) by WA method

96

42 FSA results

The FSA results were obtained using a low-energy cut-off of 300 keV for long measurements

and 400 keV for short measurements (see also Figure 319) The fits on which results are based

are shown in Figures 320 to 332 The derived activity concentrations from long and short

measurement are given in Tables 410 to 411 respectively

Sample description

Activity Concentration in (Bqkg) (for long measurement) with a cut off energy of 300 keV Full Spectrum Analysis (FSA)

S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand

61 plusmn 3 40 plusmn 01 22 plusmn 03 16

17A Westonaria sand


6B Kloof mine sand 242 plusmn 4 272 plusmn 1 194 plusmn 02 23

D6 Brick clay


5 thorium+stearic acid


Table 410 The FSA results (long measurement) uncertainties and the associated chi-square per degree of freedom obtained using cut-off energy of 300 keV for the samples indicated

97

Sample description

Activity Concentration in (Bqkg) (for short measurements) with cut off energy of 400 keV Full Spectrum Analysis (FSA)

S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand

356plusmn 33 07plusmn 03 33plusmn 03 19

17A Westonaria sand

250 plusmn 10 241 plusmn 2 21plusmn 1 22

6B Kloof mine Sand 240 plusmn 9 237plusmn 2 20plusmn 1 18

D6 Brick clay


Table 411 The FSA results (short measurements) uncertainties and the associated chi-

square per degree of freedom obtained using a cut off energy of 400 keV for the samples

indicated

98

43 Comparison of WA and FSA results

The weighted average WA results and FSA results are tabulated and juxtaposed in Tables 413

and 414 for long and short measurements respectively A comparison of the results is shown

graphically in Figures 41 to 412

iThemba LABS ERL Soil Measurements

Activity Concentration in (Bqkg) for long measurements with cut-off energy of 300 keV

Windows Analysis (WA)

Full Spectrum Analysis (FSA)

Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand

593 plusmn 15 53 plusmn 03 36 plusmn 03 61 plusmn 3 40 plusmn 01 22 plusmn 03 16

17A Westonaria sand


6B Kloof mine sand

244 plusmn 4 320 plusmn 5 21plusmn 1 242 plusmn 4 272 plusmn 1 194 plusmn 02 23

D6 Brick clay


Table 412 The activity concentrations from the two methods of analysis for long measurement

99


Activity Concentration in (Bqkg) for short measurements at the cut-off energy 400 keV

Window Analysis (WA)


Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand

54 plusmn 4 52 plusmn 05 46 plusmn 05 356plusmn 33 07plusmn 03 33plusmn 03 19

17A Westonaria Sand

216 plusmn 11 257 plusmn 6 14 plusmn 2 250 plusmn 10 241 plusmn 2 21plusmn 1 22

6B Kloof mine Sand

244 plusmn 11 277 plusmn 5 21 plusmn 2 240 plusmn 9 237plusmn 2 20plusmn 1 18

D6 Brick clay


Table 413 The activity concentrations from the two methods of analysis for short measurements

The long measurement results of these two methods (WA and FSA) were plotted on the

histograms to show the variations in activity concentrations for various samples The percent

uncertainties were also shown see Figures 41 to 412 The notations WAL WAS FSAL and

FSAS are defined as follows

WAL = Window Analysis Long (for long measurement)

WAS = Window Analysis Short (for short measurement)

FSAS = Full Spectrum Analysis (for short measurement)

FSAL = Full Spectrum Analysis (for long measurement)

100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL

Figure 41 The comparison of the three nuclides for Westonaria sand (long measurement) in both window and FSA analyses

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S

Figure 42 The comparison of the three nuclides for Westonaria sand (short measurement) in both window and FSA analyses

e s t o n a r i a s a m p l e

02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y

W A LW A SF S A LF S A S

W

40K 232Th 238U

Figure 43 The percentage uncertainties for activity concentrations as a function of nuclide for Westonaria sand sample

101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L

Figure 44 The comparison of the three nuclides for Kloof sand (long measurement) in both window and FSA analyses

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S

Figure 45 The comparison of the three nuclides for Kloof sand (short measurement) in both window and FSA analyses

K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U

Figure 46 The percentage uncertainties for activity concentrations as a function of nuclide for Kloof sand sample

102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L

Figure 47 The comparison of the three nuclides for west coast (long measurement) in both window and FSA analyses

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S

Figure 48 The comparison of the three nuclides for West coast (short measurement) in both window and FSA analyses

W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U

Figure 49 The percentage uncertainties for activity concentrations as a function of nuclide for West Coast sand sample

103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L

Figure 410 The comparison of the three nuclides for brick clay for long measurement in both window and FSA analyses

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S

Figure 411 The comparison of the three nuclides for brick clay for short measurement in both window and FSA analyses

B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U

Figure 412 The percentage uncertainties for activity concentrations as a function of nuclide for brick clay sample

104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350

Activity concentration via FSA in(Bqkg)

Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932

Figure 413 A graph showing correlation of activity concentration determined using the WAM vs FSA on average the two methods agree well within the correlation coefficient of 0932 as depicted on Figure

105

The deviation between results from the two methods for 238U concentrations (long

measurements) was found to be about 18 for the Kloof 13 for Westonaria 4 for brick

clay and 25 for West coast sand (see Figure 414) The deviations between results from long

measurement for 232Th yielded 6 for Kloof sample 5 for Westonaria sample 1 Brick

clay and 63 for West coast sand (see Appendix E for the ratios presented) The deviations

are consistently higher by these percentages for WA than FSA This trend has to do with the

fact that the uranium and thorium sources (used for FSA method) did not fill 1 litre Marinelli

beaker This could be attributed to the self-absorption effects which vary as a function of

volume The evidence of this is presented later in section 45 An attempt to study the volume

and density effects was made through the use of the Sima model [Sim92] and the results from

this modelling are presented in section 45 (see also appendix D)

The low activity West coast sample resulted in very high uncertainty in 238U activity

concentrations (see Figure 49 and 415) This was especially true for the FSA method which

has proved to find it difficult to determine the activity concentrations of low activity nuclides

This is because of the contribution of the background counts which at times are higher than

net counts especially in short measurements thus yielding a poor fit

1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K

Figure 414 The activity concentration ratipotassium long measurement for various sample

5

1 2 3 4 Kloof Westonaria Brick clay West Coast

m p le s

5

0 1 2 3 4 Kloof Westonaria Brick clay West Coast

a m p le

5


06

m p le s

os (WAFSA) of uranium thorium ands

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity

1 2 3 Kloof Westonaria Brick clay 4

232Th


40K


Figure 415 The activity concentration ratios (WAFSA) of uranium thorium and potassiumfrom short measurements for various samples The ratio for the 238U (West coast sample) isnot shown

107

Method Advantages Disadvantages Significant source of

uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum

Table 414 Advantages and disadvantages for the two methods including the best measurement times required for the activity concentration determination For samples where 40K and 232Th have the same activity concentration the 40K line is ten times

stronger than the 232Th line [Dem97] In case the 232Th content is several orders of magnitude

larger it becomes virtually impossible to determine the 40K content accurately since the peaks

are very close to each other

The results of the high thorium content are tabulated in Table 415 for the evidence of that

For the FSA this summing effect is not a problem since all the peaks are considered for the

determination of the content of these two nuclides that is the 40K and 232Th In the WA the

14608 keV peak is confused with the 14592 keV one

108

40K 1 plusmn 4 31 plusmn 5

238U 08 plusmn 05 12 plusmn 1

3954 plusmn 03 469 plusmn 8

FSA activity concentrations (Bqkg)

WA activity concentrations (Bqkg) Nuclide

232Th

Table 415 The results of sample 5 a high thorium content sample

050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA

Figure 416 Activity concentration of nuclides for the high thorium content sample

109

bull Thorium sample

As discussed in chapter 2 the thorium + stearic sample was made up using stearic acid and

IAEA reference material (RGTh-1) having an activity concentration of 3250 Bqkg (see Table

24) The sample was prepared in such a way that the activity concentration of 232Th in the

sample was 5000 plusmn 05 Bqkg [Jos04]

The WA and FSA results for this sample allow us to compare WA and FSA derived 232Th

concentrations with what is expected As can be seen in Table 415 the WA yields a result of

469 Bqkg which is 9 smaller than expected The FSA gives the result of 395 Bqkg which

is 21 smaller than expected It is clear from Figure 331 that the counts in FSA fit spectrum

are generally higher than in the measured spectrum in regions outside photo peaks This

happens since the full-energy peak efficiency (also termed the photopeak efficiency) is higher

in the case of thorium sample since it has such a low density (~07 gcm3) resulting in a higher

peak to total ratio (ie relatively more counts inside than outside the photopeak) Since the

FSA procedure involves the minimisation of reduced chi-square the photopeaks are fitted

preferentially since a misfit in the region of a photopeak contributes significantly to reduced

chi-square

44 Discussion of WA Results

Counting uncertainties in environmental measurements are usually high such that coincident

summing corrections might be neglected [Gar01] But the lines that are prone to coincident-

summing6 such as the 609 keV were still avoided for purpose of reducing the systematic error

At present the ERL at iThemba LABS has a study going on about the prominent lines that are

prone to the coincidence-summing problem Other lines that are prone to the coincident-

6 This is when γ-rays are emitted in cascades from a nucleus and thus detected as one peak

110

summing like the 9112 keV 9690 keV from 228Ac and 7273 keV due to 212Bi might in future

be omitted [Gar01]

Accumulation of good statistics is required for the reliability of this method This was

demonstrated by comparing the uncertainties associated with measurements of varying

duration Results from shorter measurements were more uncertain than those from long ones

(see Figures 434649 and 412)

45 Discussion of FSA Results

Contrary to WA which only uses the data in a number of peaks for analysis FSA includes all

the spectral information in the data analysis The increased amount of information will

decrease the statistical uncertainties in the method thus giving this method an advantage

A practical problem of the FSA method might be the fact that small gain drifts may occur

resulting in the slight shifts and broadening of peaks

The results for this method are given for the cut-off energy of 300 keV for the long

measurement and for shorter measurement a lower cut-off energy of 400 keV and higher cut-

off energy of 1600 keV were used to exclude high energy background counts

This particular cut-off energy was chosen because of the poor fit as observed for low energies

(see Figures 320 and 321) This is reflected by the high values of χ2ν Figure 320 shows an

under-estimation of the measured spectrum with a chi-square 25 at the cut-off energy of 300

keV for a typical spectrum of Kloof sample 6 This under prediction at lower energies is

attributed to the self-absorption effects

From Table 24 it is clear that the Marinelli beakers fillings were not the same in volume

therefore this has a consequence on the measurement result due to these volume effects

which are related to self-absorption effects Figures 417 418 are the results showing the

transmission factors from the Sima calculations for various samples with different densities as

111

discussed in Appendix D while Figure 419 illustrates the volume effects for the uranium

source Debertin and Ren did a similar study [Deb89]

The poor reproduction of the FSA at energies less than 300 keV led to the studying of self-

absorption effects based on the Sima model

Self-absorption is the removal of γ-ray by material in the sample itself The effect increases for

lower energies (lt 300 keV) and with the atomic number of an element [Dem97]

Figures 417 and 418 show the results of the effect of density on the transmission factors (see

Appendix D for discussion on this) while Figure 419 shows the volume effect on the

transmission factors

112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)Water(10)

Figure 417 Calculated transmission factors for different densities for a 1000 cm3

Marinelli as a function of γ-ray energy the legends shows the three reference sources

which are Potassium Chloride (KCl) uranium and thorium together with water and sand

at various densities (densities are shown by the numbers in brackets in the legends)

113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)

Figure 418 The transmission factor for a 500 cm3 Marinelli at different densities as a function of γ-ray energy

114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml

Figure 419 The volume effect on the transmission factor for different fillings (with sand of density 16 gcm3) of Marinelli as a function of γ-ray energy

115

During the determination of the detection efficiency an error may occur due to the difference

in the densities of the standard source and the sample This effect can be verified from the

Figure 417 In this Figure it is clear that at lower energies samples with high densities such as

that of sand at 16 gcm3 get attenuated even more while the less dense samples such as water

at a density of 1 gcm3 get attenuated even less This trend is strong at energies less than 300

keV and at higher energies is almost negligible The other difference is due to the atomic

number this difference can be witnessed by the KCl which gets attenuated more at lower

energies than sand even if its density is less than that of sand This is simply because KCl has

an effective atomic number Z greater than that of SiO2 which is a major constituent of sand

Most of the photon attenuation occurs at low energy with Marinelli beaker filled to its full

capacity while at lower volumes there is less attenuation this is because it takes photons far

away from the detector even more time to arrive at the detection point and hence they get

attenuated on their path see Figure D1 (Appendix D) for the variations in the filling of the

beaker

The under prediction of the fit at the continuum for the FSA method of analysis is attributed

to this concept especially because the source volumes were plusmn 400ml for thorium and

uranium while samples had volumes close to 100 ml see Tables 23 and 24 for details

Different filling heights of the Marinelli beaker yield different effective thickness which were

used to calculate the transmission factors as in the Figure D1 (see also Table D1 in Appendix

D) The percentage difference according to these volume differences was calculated for full

(1000 ml) and half-full (500 ml) Marinelli beaker These percentage differences are plotted in

Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence

Figure 420 The differences in the transmission factors of (Westonaria sand) with regard to full and half full Marinelli beaker as a fuction of energy

On interpolation the percent difference due to volume for the 14608 keV line was found to be

about 15 The percent difference D was calculated as follows

100 timesminus

=full

halffull

TTT

D (41)

where Tfull and Thalf are transmission factors for a full and half-full Marinelli beakers

respectively These self-absorption effects are of major concern this can be seen in Figure 319

for energies below 300 keV therefore another approach of defining these effects will be to

describe the probabilities of the interaction of γ-ray with matter inside both the detector and

Marinelli beaker This will be done by following a γ-ray photon of a particular energy inside the

Marinelli beaker until the detector absorbs it Two possibilities were taken into consideration

in particular photoelectric absorption and Compton scattering

117

Consider the Figure 421 Detector

5

4

Origin of Incoming γ-rayphoton

2

1 3

Electron

Figure 421 A filled Marinelli beaker showing an incoming photon and possibilities of interaction in both the beaker and detector The incoming γ-ray of a particular energy interacts with an electron of the sample in the

Marinelli beaker and there are several possibilities by which it can interact These are

photoelectric absorption (1) and Compton scattering (2) and another Compton scattering (3)

The scattering photon could get deviated again leading to photoelectric absorption in the

detector as in (4) Process (3) is more dominant when the sample is denser while process (2) is

most likely when the sample is less dense The incoming γ-ray photon in (4) will lose some

energy proportional to the density of the sample and thus contributing more to low energy

photons at the Compton continuum This explains the reason why the fit at the region from

50 keV to 300 keV is underestimated at the continuum for sample of higher density such as in

Figure 320 (a) Process (4) explains the overestimation of the lower density sample in Figure

320 (b) Another process is direct photoelectric absorption (5) on a crystal

118

CHAPTER 5

Conclusion This chapter reviews the results of this study and future work on the study is suggested

51 Outlook

This study introduced a novel technique that is the FSA method of analysis to the analysis of

soil spectra using HPGe detector in the ERL at iThemba LABS to complement the

conventional Window Analysis method

Although a correlation was obtained between these two methods of analysis the interpretation

of the results was found to be difficult since the volume of reference 238U and 232Th material

used to obtain standard spectra were only 400 ml whereas the samples to be measured were all

close to the full capacity of Marinelli beakers (volume ~ 900 ml) This resulted in the different

self-absorption effects during the measurement of standard spectra than during the

measurement of sample spectra

Furthermore the difference in volume also leads to the different efficiencies caused by the

change in the geometry For a full Marinelli beaker the average distance from the sample to the

detector is larger than in the 400 ml case In order to avoid the systematic error associated with

this volume effect it is recommended new standard spectra be obtained by measuring

Marinelli beakers filled with reference 238U and 232Th material to obtain constant geometry In

order to accomplish this additional reference material will have to be purchased After these

new standard spectra are obtained the only significant remaining effects that need to be

considered is that associated with density and the effective charge of the material

The model of Sima et al [Sim92] used to calculate the self-absorptions in Marinelli beakers

was found to under-predict the volume effect observed in this work There is therefore scope

to improve this model An alternative to this is to use a Monte Carlo simulation approach

119

The FSA method has shown some difficulty in determining activity concentrations of low

activity samples especially if the background counts are higher than the net counts From

Figures 43 46 49 and 412 in Chapter 4 it is clear that measuring times have to be increased

for WA and FSA short measurements in order to obtain good counting statistics with these

methods The uncertainties increase with a decrease in activity concentrations and this is due

to the contribution of the background counts This can be witnessed in the results of low

activity samples such as the West coast sand sample in Figure 49 where uncertainties

presented for both methods are high

In the FSA method of analysis all the information is included in the spectrum in contrast to

the choosing of regions of interest of prominent peaks in the WA Ignoring the Compton

continuum in the WA simply implies throwing away some counts that can be used for data

analysis

In order to minimise the inevitable self-absorption effects in an attempt to obtain optimal

results in this study the cut-off energy of 300 and 400 keV which gave best least square fit

were therefore chosen

In future if more focus could be put on the absorption effects at low energies for the FSA

method then the accuracy and precision of this technique could improve even further

Perhaps with the help of simulations from software programs such as the Monte Carlo N

Particle extension transport code (MCNPX) which the ERL has at the moment introduced

an effort could be made in the future to understand these effects even better

120

Appendix A

A-1 Some Formulae for combining uncertainties

Type of equation from which

Result R is to be calculated

Formula for calculating the

uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B

Where a and b are constants ∆R= 22 )()( BbAa ∆+∆

R = Ap

Where p is a constant

R = a AP

Where a and p are constants AAP

RR ∆

=∆

R = AP Bq

Where p and q are constants

22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆

Table A1 the table shows some of the equations used in the calculation of the uncertainty ∆R derivation from [Kno79]

121

A-2 Means and Standard deviation

The mathematical operation commonly applied to a set of measured or deduced values

( i of a quantity X is to derive an average or mean value ix )21 n= x and an estimate of the

uncertainty of x s( x ) If the values to be averaged have no associated uncertainties the

arithmetic mean is simply given as

sum=

=n

iix

nx

1

1 (A1)

or otherwise the average is calculated as the weighted mean

(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(

were is a weighting factor defined as the inverse of the squared standard deviation iw

If the parent distribution is a Gaussian or Poisson distribution and if the sample of the n values

has been obtained from repeated measurements under identical measuring

conditions the arithmetic mean of equation (A1) is the best estimate of the expectation value

m of the parent distribution With increasing sample size the arithmetic mean

ni xxx 2

n x approaches

m[Deb88]

The variance σ2 of the parent ditribution is estimated by the experimental or sample varience

2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)

The relative standard deviation s(x) x is also called the variation coefficient υ

122

The experimental variance of the mean s2( x ) denoted by var( x ) is smaller than s2(x) by a

factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)

Many counting experiments produce only a single result say N counts In these cases we take

N as the estimate of m since m = σ2 for a Poisson distribution N is taken as experimental

standard deviation s(N)

If we have a set of values each of which has an associated variance and if these

variances are not equal the weighted mean defined in (A1) is a better estimate for m than the

arithmetic mean For the weighting factors the reciprocals of the variances are taken ie

ix is 2

ii sw 21=

The variance of x may be derived in two ways The external variance is obtained in analogy to

equation (A3) with weighting factors included ie

sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)

The internal variance is

sum=

= n

iiw

xs

1

2 1)2( (A6)

123

The magnitude of χ2R the reduced chi-square which is the measure of the goodness of fit to

the data is given by

2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)

where χR2 is expected to be of the order of unity for a perfect fit to the data [Deb88]

124

Appendix B FORTRAN program

(program used for converting channel numbers to equivalent energy in keV)

c Note that E = a + b Ch or Ch = Eb - ab c c therefore the channel that corresponds to energy i keV c c is given by Ci=ib - ab c and C(i+1) = (i+1)b - ab c Here Ci and Ci+1 are floating point numbers c When we transform to the integer value one will still c get that Ci and Ci+1 may cover two or three channels c c change energy scale c note that n KeV is in ch n+1 dimension eold(5000)ich(5000)countn(5000)cntnew(5000) open(unit=5file=inputfiletxt) open(unit=7file=outputfiledat) do 50 i=17 c read(5) c 50 continue c read livetime read(545)time

45 format (26xle167) read(5)

read(555) a read(555)b read(555)c 55 format (55xle167) c imax=4100 write() imaxabc do 70 k=14 read(5) 70 continue do 200 i=1imax read(5)ichcountn(i) 200 continue write()(iCH(i)eold(i)countn(i)) 300 continue

c now change the energy scale for b=06471 newmax=imaxb+10 do 1000 i=0newmax

125

Epold1=ib - ab Epold2=(i+1)b - ab Else Epold1=(-b+sqrt(bb-4c(a-i)))(20c) Epold2= (-b+sqrt(bb-4c(a-i-1)))20c) endif c j=int(Epold1) jp1=j+1 jp2=j+2 jp3=j+3 jprime=int(Epold2) cntnew(i)=(jp1-Epold1)countn(jp1) c if ((jprime-j)eq1) then cntnew(i)=cntnew(i)+(epold2-jp1)countn(jp2) else c if it spans 3 channels cntnew(i)=cntnew(i)+countn(jp2)+(Epold2-jp2)countn(jp3) endif 1000 continue c print do 2000 i=1newmax write(7)icntnew(i) 2000 continue end

126

Appendix C Background Spectrum

0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd

Figure C-1 The background spectrum used in this study It was obtained by measuring a Marinelli beaker filled with tap water

127

Appendix D Self-absorptions effects (by Modelling of the γ-ray transmission through a Marinelli beaker)

According to the model developed by Sima [Sim92] and used here the γ-ray transmission

through a sample-filled Marinelli beaker can be calculated using the expression

teF

t

a micromicro

microminusminus=

1)( (D1)

where F is the transmission factor which is a function of the γ-ray linear attenuation

coefficient and the γ-ray energy t is the effective thickness (of the sample being measured) as

viewed from a small spherical detector This detector is placed in relation to the Marinelli

beaker as shown in Figure D1 The model assumes the detector to be a spherical point

raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm

Figure D1 The Marinelli Beaker with a spherical detector model at the center

The filling of the re-entrant hole he-hi approximately equals the thickness re-ri This thickness

was determined according to the model developed by Sima [Sim92] and the value of this

thickness was recorded for different filling heights These dimensions are tabulated in Table

D1

The effective thickness t can then in principle be determined as follows

int

intΩ

Ω=

d

dl )(θt (D2)

where l(θ) is the thickness of the sample corresponding to the angle θ (see Figure D1) and

denotes integration over the solid angle subtended by the sample

int

Sima showed that t can then be calculated from the expression

t (D3) )]()()()([10201 hrfhrfhrfhrf iiee minusminus+

Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2

)(tan)( 21 ++= minus hrhrhgrhrf ] (D5)

129

with r and h being the dimensions of the model Marinelli beaker shown in Figure D1 The

values of r and h for the Marinelli beaker used here are given in Table D3 For a fully filled

Marinelli beaker the effective thickness t of the sample was found to be 26 cm The effective

thickness for the beaker filled to 500 ml was also calculated (see Table D1)

Volume of sand in Marinelli

beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)

Effective thickness t (mm)

1000

111

259

500

73

159

Table D1 Results of calculations of the effective thickness t for two Marinelli volumes

γ-ray mass attenuation (microρ )coefficients in various materials can be found in compilation of

Huumlbbel [Hub82] In the use of a generic compound XY where X and Y are two different

elements one can calculate the attenuation coefficient for the sample using the expression

))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro

ρmicroρmicroρmicro

ρmicroρmicro

++

+=( (D5)

An example in this case is silicon oxide (SiO2) which is a major constituent of soil We used

the Sima formula to calculate the transmission through a Marinelli beaker filled with water

KCl generic sand 232Th and 238U sources Calculations were made from 50 keV to 2 MeV in

steps of 50 keV The assumed elemental composition of the 238U and 232Th are given in the

130

IAEA manual [RL148] however we assumed the SiO2 to be the major constituent for these

two elements

The calculated transmission factors are shown in Table D2

Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy

(keV) Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923

Table D2 A table of the mass attenuation coefficients and the transmission factors

131

Beaker Dimensions

re ri r hi h2 he h1 h0 66 mm

443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm

Table D3 The dimensions of the full Marinelli Beaker used in the iThemba ERL (for a half full Marinelli (500ml) he = 73 mm)

132

Appendix E Ratios of activity concentrations

Sample type Nuclide Long measurement activity concentration

ratios (WAFSA)

Short measurement activity concentration

ratios (WAFSA) 40K 097 plusmn 005 15 plusmn 02

232Th 16 plusmn 03 14 plusmn 02 West Coast sand

238U 125 plusmn 008 74 plusmn 30 40K 101 plusmn 002 086 plusmn 006

232Th 106 plusmn 006 07 plusmn 01 Westonaria sand


232Th 106 plusmn 004 108 plusmn 01 Kloof mine Sand


232Th 101 plusmn 006 093 plusmn 005 Brick clay

238U 104 plusmn 005 104 plusmn 005 Table E1 The ratios of the activity concentrations (WAFSA) and the associated uncertainties for samples used in the study The ratios are shown for both short and long measurements

133

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[Bei87] Beiser AConcepts of Modern Physics fourth edition McGraw-Hill Book Co

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[Chu94] Chuma JL Physica Reference Manual 4004 Wesbrook Mall Vancouver BC

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[Cre87] Creagh DC The Resolution of Discrepancies in Tables of photon Attenuation

Coefficients Radiation Physics proceedings of the International Symposium on

Radiation Physics University di Ferrara Ferrara Italy (1987)

[Deb88] Debertin K Helmer RG Gamma - and X -Ray Spectroscopy with

semiconductor detectors Elsevier science publishers BV Amsterdam (1988)

[Deb89] Debertin K and Ren JMeasurement of Activity of Radioactive Samples in Marinelli

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[Dem97] De Meijer RJ Stapel C Jones DG Roberts PD Rozendaal A MacDonald

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[Dem98] De Meijer RJ Heavy Minerals From Edelstein to Einstein J Geochemical

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[Dry89] Dryak P Kovar P Plchova L Suran J Correction for the marinelli geometry J

Radioanal Nucl Chem letters 135 281 (1989)

134

[EML97] Environmental Measurements Laboratory Dept of Energy (USA) HASL-30028th

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[Eva55] Evans RDThe Atomic Nucleus McGraw-Hill New York (1955)

[Fel92] Felsmann M Denk HJ Efficiency Calibration of Germanium Detectors with Internal

Standards J RadioanalNucl Chem 157 47 (1992)

[Fuumll99] Fuumlloumlp M Portable gamma spectrometers for environmental and industrial applications at the

institute of preventative and clinical medicine in Bratislava Bratislava Slovakia Industrial

and environmental applications of nuclear techniques report of a workshop held in

Vienna 7-11 September 1998 International Atomic Energy Agency (IAEA)

(1999)

[Gar01] Garcia-Talavera M Laedermann JP Decombaz M Daza MJ Quintana B

Coincidence summing corrections for the natural decay series in γ-ray spectrometry Journal of

Radiation and Isotope 54 769 (2001)

[Gil95] Gilmore G Hemingway JD Practical gamma-ray spectrometry John Wiley amp

Sons New York (1995)

[Hew85] Hewitt PG Conceptual Physics Fifth edition City College of San Francisco (1985)

[Hen01] Hendriks PHGM Limburg J de Meijer RJ Full-spectrum analysis of natural

gamma-ray spectra J Environmental Radioactivity 53 365 (2001)

[Hen03] Hendriks P In-depth γ-ray studies Borehole measurements Rijksuniversiteit

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environment (Technical report series No295) (1989)

[ISO03] Draft international standard ISODis 18589-1 Measurement of radioactivity in the

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[Jos04] Joseph AD iThemba LABS South Africa (Private communication) (2004)

[Kno79] Knoll GF Radiation detection and measurement John Wiley amp Sons New York

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[Kno00] Knoll GF Radiation detection and measurement third edition John Wiley amp Sons

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[Leo87] William R Leo Techniques for nuclear and particle physics experiments Springer-Verlag

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[Sta97] Stapel C Limburg J de Meijer RJ Calibration of BGO scintillation detectors in a bore

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[USR98] Germanium detectors Users Manual Canberra industries 800 Research Parkway

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[www01] wwwscescapenet~woodselementspotassiumhtml taken on 17082004

[www02] wwwdohwagovehprpairFact taken on 4092003

138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

Library

Document is released

Declaration

I the undersigned declare that the work contained in this thesis is my own original work and

has not previously in its entirety or in part been submitted at any university for a degree

Signature

Date

ii

Acknowledgements




















iii



Katse Piet Maphoto

Abstract















conclusion




iv









short measurements







v

Table of Contents




112 Decay modes3

113 Decay rates5












vi



17 Thesis outline24





213 Electronics28










vii





41 WA Results88

42 FSA Results97





51 Outlook119

APPENDICES






viii


ix

List of Tables


1 m deep 12






calibrations 35









x










by WA method 93









indicated 97

xi



indicated 98



measurement 100





121






xii

LIST OF FIGURES












scale 19



iThemba LABS 26


xiii


detector (B) 28












entrant hole 42





curve

xiv

49

cy

51


calibration 53



















spectrum S 65

xv



















xvi













a fit 85







xvii





















0932) 105

xviii









energy 114









xix

C h a p t e r 1

1 Introduction





















1
























NAZ X



R = R0A13 (11)

2











112 Decay modes





42

42YX A

ZAZ




anti-neutrino


11

10 (13)

3



eA


011 (14)








10

11


(16) eA


minus011









4



(17) eA


minusminus 1

01

113 Decay rates





NdtdN λminus= (18)





λ

2ln21 =t (110)


represented by


5

















way into the earth




and 131I)

6














dN1 = -λ1N1dt (112)



dN2 = (λ1N1 -λ2N2)dt (113)



chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7








t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-





β+

0001




rs

8


45x109

y

117 m



actinium (Ac) 89


francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85


polonium (Po) 84




206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny


9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny


10


























11

















[Van02b]




12

















13








by








γ-ray

Ee

Eγ Nucleus


14

Nucleus

Kα X-ray

γ-ray Electron









given by



photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)











Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ


16














posit


elect511 keV


E

Eγ

ron

ron 511 keV


17



















)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)


target element

18







bull In-situ






19







A

NNN

AN O

O

ff Φbull

Φbull= (120)









being measured






20
















Applied Radiometry



21









Quartz 116 (8) 2 (2) lt 9


Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)


22


























23
















established

17 Thesis outline





24

Chapter 2





















25

211 Physical layout




NIM crate


filling)








26



bull Lead Castle









shown in Appendix C


27


A B







213 Electronics




a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector


data

bull Detector







[USR98]

29




h+

Valence band

Conduction bande-

Eg






30










temperatures




31

bull Detector bias








bull Preamplifiers











bull Amplifier




32
















below


Monitor



33

214 Figure of merit











BchAE += )( ( 21)






follows

(22) CchBchAE ++= )()( 2

34





below

Decay series









35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd


Energy keV

36

energ

y







R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174



37







resolution [Kno79]









38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409















39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI





A ROI C G

30394 511 87 44482









40



high














Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes


067734 28740 1000 0677 Yes


41













42











powder) reference

bull WA






bull FSA





43


method


Mass (kg)

Volume (ml)

Density (gcm3)



232Th FSA IAEA (RGTh) 05157 400 13 3250







24 Data acquisition



software used



44




KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026



Code Elapsed

real time(s)

Elapsed live

time(s)


Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594


28800 28740


116322 116312


45

Chapter 3

Data Analysis




31 Window Analysis



)(EtiB

iN

LMrC

kgBqAε

prime= (31)













46

(32) sum=

=

=ei

siig CC


equation

(33) sum=

=

=ei

siCic CC











ibB

CiNiN C

LL

C

minus=primeC (35)



47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum





48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6










49






b

EEa

=

0

ε (36)


parameters [Dry89]


ln (37) 0

lnlnEEba +=ε

50



efficiencies


2


Reference source 3


4


between 2 amp 4 5



efficiency

7


51








Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series



40K Series

40K 14608 01066




52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)


53






in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241







54








Mmn = (38)




21

2lnt







equation 310

55

ALMr

C

tB 1461

1461 =ε (310)









56


310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572


57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392


002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)


58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)


59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)


-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)


U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)



60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252


- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )


a = 51057 b = -08147

2 4 6 8 1 0

ln(E)


61










iNC∆ ibC∆




b

iNrel r

C prime=ε (312)


22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62




baE=ε


22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε











are arrived at

63




















64




M(j)

j S S











65



Standard spectrum







66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10


Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)


Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)












sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)










)(iw



70


Let


BB ii ∆=plusmnΒ



22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)



22

∆+

∆=

B

i

A

ii t

BtA

σ (318)


deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71





w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)



02

=partpart


72








0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e


73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)


Energy (keV)


74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)


75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)


76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500


79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000


81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd


82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd








acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured


0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured



85




CCC ∆+= 01 (323)







C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)




2

00

11

2 )()(

part


== CCCxf

Cxfyw kkk

N

kk

N

kkδ


2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86




and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1




and E2 where





Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ



87

Chapter 4




41 WA results





(Bqkg)

Full-energy peak

Absolute efficiency




320 plusmn 5


21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940


88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration


263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940


89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940


90






30 plusmn 14


55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940


91






13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940


92



Nuclide Energies





277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986


93







257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940


94



(Bqkg)


efficiency




52 plusmn 05


46 plusmn 05


95

Nuclide Energies





32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986


96

42 FSA results





Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay





97

Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay




indicated

98









Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand


17A Westonaria sand


6B Kloof mine sand


D6 Brick clay



99





Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand


17A Westonaria Sand


6B Kloof mine Sand


D6 Brick clay











100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S



02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y


W

40K 232Th 238U


101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350


Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932


105

















1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K


5


m p le s

5


a m p le

5


06

m p le s


0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity


232Th


40K



107


uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum









108






232Th


050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA


109

bull Thorium sample















chi-square








110


be omitted [Gar01]























111










112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor






113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)


114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml


115














beaker








Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence




100 timesminus

=full

halffull

TTT

D (41)








117


5

4


2

1 3

Electron












118

CHAPTER 5


51 Outlook





















119












analysis









120

Appendix A





uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B


R = Ap


R = a AP


RR ∆

=∆

R = AP Bq


22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆


121






sum=

=n

iix

nx

1

1 (A1)


(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(






ni xxx 2

n x approaches

m[Deb88]


2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)


122


factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)







ix is 2

ii sw 21=



sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)


sum=

= n

iiw

xs

1

2 1)2( (A6)

123



2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)


124







125


126


0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd


127




teF

t

a micromicro

microminusminus=

1)( (D1)





raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm





D1


int

intΩ

Ω=

d

dl )(θt (D2)



int



Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2


129






beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)


1000

111

259

500

73

159





))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro


ρmicroρmicro

++

+=( (D5)





130


two elements


Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy


(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923


131

Beaker Dimensions


443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm


132



ratios (WAFSA)











133



Singapore (1987)

















134


edition (1997)








(1999)











135








(1979)


New York (2000)


(1988)


Berlin (1987)


(2001)



thesis (2001)

136



















137





Meriden CT 06450 (1998)





unpublished (2002)







138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

Library


Acknowledgements




















iii



Katse Piet Maphoto

Abstract















conclusion




iv









short measurements







v

Table of Contents




112 Decay modes3

113 Decay rates5












vi



17 Thesis outline24





213 Electronics28










vii





41 WA Results88

42 FSA Results97





51 Outlook119

APPENDICES






viii


ix

List of Tables


1 m deep 12






calibrations 35









x










by WA method 93









indicated 97

xi



indicated 98



measurement 100





121






xii

LIST OF FIGURES












scale 19



iThemba LABS 26


xiii


detector (B) 28












entrant hole 42





curve

xiv

49

cy

51


calibration 53



















spectrum S 65

xv



















xvi













a fit 85







xvii





















0932) 105

xviii









energy 114









xix

C h a p t e r 1

1 Introduction





















1
























NAZ X



R = R0A13 (11)

2











112 Decay modes





42

42YX A

ZAZ




anti-neutrino


11

10 (13)

3



eA


011 (14)








10

11


(16) eA


minus011









4



(17) eA


minusminus 1

01

113 Decay rates





NdtdN λminus= (18)





λ

2ln21 =t (110)


represented by


5

















way into the earth




and 131I)

6














dN1 = -λ1N1dt (112)



dN2 = (λ1N1 -λ2N2)dt (113)



chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7








t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-





β+

0001




rs

8


45x109

y

117 m



actinium (Ac) 89


francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85


polonium (Po) 84




206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny


9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny


10


























11

















[Van02b]




12

















13








by








γ-ray

Ee

Eγ Nucleus


14

Nucleus

Kα X-ray

γ-ray Electron









given by



photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)











Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ


16














posit


elect511 keV


E

Eγ

ron

ron 511 keV


17



















)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)


target element

18







bull In-situ






19







A

NNN

AN O

O

ff Φbull

Φbull= (120)









being measured






20
















Applied Radiometry



21









Quartz 116 (8) 2 (2) lt 9


Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)


22


























23
















established

17 Thesis outline





24

Chapter 2





















25

211 Physical layout




NIM crate


filling)








26



bull Lead Castle









shown in Appendix C


27


A B







213 Electronics




a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector


data

bull Detector







[USR98]

29




h+

Valence band

Conduction bande-

Eg






30










temperatures




31

bull Detector bias








bull Preamplifiers











bull Amplifier




32
















below


Monitor



33

214 Figure of merit











BchAE += )( ( 21)






follows

(22) CchBchAE ++= )()( 2

34





below

Decay series









35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd


Energy keV

36

energ

y







R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174



37







resolution [Kno79]









38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409















39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI





A ROI C G

30394 511 87 44482









40



high














Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes


067734 28740 1000 0677 Yes


41













42











powder) reference

bull WA






bull FSA





43


method


Mass (kg)

Volume (ml)

Density (gcm3)



232Th FSA IAEA (RGTh) 05157 400 13 3250







24 Data acquisition



software used



44




KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026



Code Elapsed

real time(s)

Elapsed live

time(s)


Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594


28800 28740


116322 116312


45

Chapter 3

Data Analysis




31 Window Analysis



)(EtiB

iN

LMrC

kgBqAε

prime= (31)













46

(32) sum=

=

=ei

siig CC


equation

(33) sum=

=

=ei

siCic CC











ibB

CiNiN C

LL

C

minus=primeC (35)



47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum





48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6










49






b

EEa

=

0

ε (36)


parameters [Dry89]


ln (37) 0

lnlnEEba +=ε

50



efficiencies


2


Reference source 3


4


between 2 amp 4 5



efficiency

7


51








Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series



40K Series

40K 14608 01066




52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)


53






in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241







54








Mmn = (38)




21

2lnt







equation 310

55

ALMr

C

tB 1461

1461 =ε (310)









56


310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572


57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392


002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)


58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)


59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)


-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)


U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)



60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252


- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )


a = 51057 b = -08147

2 4 6 8 1 0

ln(E)


61










iNC∆ ibC∆




b

iNrel r

C prime=ε (312)


22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62




baE=ε


22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε











are arrived at

63




















64




M(j)

j S S











65



Standard spectrum







66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10


Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)


Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)












sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)










)(iw



70


Let


BB ii ∆=plusmnΒ



22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)



22

∆+

∆=

B

i

A

ii t

BtA

σ (318)


deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71





w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)



02

=partpart


72








0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e


73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)


Energy (keV)


74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)


75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)


76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500


79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000


81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd


82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd








acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured


0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured



85




CCC ∆+= 01 (323)







C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)




2

00

11

2 )()(

part


== CCCxf

Cxfyw kkk

N

kk

N

kkδ


2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86




and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1




and E2 where





Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ



87

Chapter 4




41 WA results





(Bqkg)

Full-energy peak

Absolute efficiency




320 plusmn 5


21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940


88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration


263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940


89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940


90






30 plusmn 14


55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940


91






13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940


92



Nuclide Energies





277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986


93







257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940


94



(Bqkg)


efficiency




52 plusmn 05


46 plusmn 05


95

Nuclide Energies





32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986


96

42 FSA results





Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay





97

Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay




indicated

98









Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand


17A Westonaria sand


6B Kloof mine sand


D6 Brick clay



99





Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand


17A Westonaria Sand


6B Kloof mine Sand


D6 Brick clay











100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S



02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y


W

40K 232Th 238U


101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350


Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932


105

















1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K


5


m p le s

5


a m p le

5


06

m p le s


0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity


232Th


40K



107


uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum









108






232Th


050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA


109

bull Thorium sample















chi-square








110


be omitted [Gar01]























111










112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor






113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)


114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml


115














beaker








Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence




100 timesminus

=full

halffull

TTT

D (41)








117


5

4


2

1 3

Electron












118

CHAPTER 5


51 Outlook





















119












analysis









120

Appendix A





uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B


R = Ap


R = a AP


RR ∆

=∆

R = AP Bq


22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆


121






sum=

=n

iix

nx

1

1 (A1)


(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(






ni xxx 2

n x approaches

m[Deb88]


2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)


122


factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)







ix is 2

ii sw 21=



sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)


sum=

= n

iiw

xs

1

2 1)2( (A6)

123



2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)


124







125


126


0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd


127




teF

t

a micromicro

microminusminus=

1)( (D1)





raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm





D1


int

intΩ

Ω=

d

dl )(θt (D2)



int



Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2


129






beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)


1000

111

259

500

73

159





))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro


ρmicroρmicro

++

+=( (D5)





130


two elements


Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy


(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923


131

Beaker Dimensions


443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm


132



ratios (WAFSA)











133



Singapore (1987)

















134


edition (1997)








(1999)











135








(1979)


New York (2000)


(1988)


Berlin (1987)


(2001)



thesis (2001)

136



















137





Meriden CT 06450 (1998)





unpublished (2002)







138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

Library




Katse Piet Maphoto

Abstract















conclusion




iv









short measurements







v

Table of Contents




112 Decay modes3

113 Decay rates5












vi



17 Thesis outline24





213 Electronics28










vii





41 WA Results88

42 FSA Results97





51 Outlook119

APPENDICES






viii


ix

List of Tables


1 m deep 12






calibrations 35









x










by WA method 93









indicated 97

xi



indicated 98



measurement 100





121






xii

LIST OF FIGURES












scale 19



iThemba LABS 26


xiii


detector (B) 28












entrant hole 42





curve

xiv

49

cy

51


calibration 53



















spectrum S 65

xv



















xvi













a fit 85







xvii





















0932) 105

xviii









energy 114









xix

C h a p t e r 1

1 Introduction





















1
























NAZ X



R = R0A13 (11)

2











112 Decay modes





42

42YX A

ZAZ




anti-neutrino


11

10 (13)

3



eA


011 (14)








10

11


(16) eA


minus011









4



(17) eA


minusminus 1

01

113 Decay rates





NdtdN λminus= (18)





λ

2ln21 =t (110)


represented by


5

















way into the earth




and 131I)

6














dN1 = -λ1N1dt (112)



dN2 = (λ1N1 -λ2N2)dt (113)



chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7








t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-





β+

0001




rs

8


45x109

y

117 m



actinium (Ac) 89


francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85


polonium (Po) 84




206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny


9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny


10


























11

















[Van02b]




12

















13








by








γ-ray

Ee

Eγ Nucleus


14

Nucleus

Kα X-ray

γ-ray Electron









given by



photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)











Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ


16














posit


elect511 keV


E

Eγ

ron

ron 511 keV


17



















)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)


target element

18







bull In-situ






19







A

NNN

AN O

O

ff Φbull

Φbull= (120)









being measured






20
















Applied Radiometry



21









Quartz 116 (8) 2 (2) lt 9


Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)


22


























23
















established

17 Thesis outline





24

Chapter 2





















25

211 Physical layout




NIM crate


filling)








26



bull Lead Castle









shown in Appendix C


27


A B







213 Electronics




a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector


data

bull Detector







[USR98]

29




h+

Valence band

Conduction bande-

Eg






30










temperatures




31

bull Detector bias








bull Preamplifiers











bull Amplifier




32
















below


Monitor



33

214 Figure of merit











BchAE += )( ( 21)






follows

(22) CchBchAE ++= )()( 2

34





below

Decay series









35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd


Energy keV

36

energ

y







R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174



37







resolution [Kno79]









38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409















39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI





A ROI C G

30394 511 87 44482









40



high














Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes


067734 28740 1000 0677 Yes


41













42











powder) reference

bull WA






bull FSA





43


method


Mass (kg)

Volume (ml)

Density (gcm3)



232Th FSA IAEA (RGTh) 05157 400 13 3250







24 Data acquisition



software used



44




KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026



Code Elapsed

real time(s)

Elapsed live

time(s)


Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594


28800 28740


116322 116312


45

Chapter 3

Data Analysis




31 Window Analysis



)(EtiB

iN

LMrC

kgBqAε

prime= (31)













46

(32) sum=

=

=ei

siig CC


equation

(33) sum=

=

=ei

siCic CC











ibB

CiNiN C

LL

C

minus=primeC (35)



47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum





48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6










49






b

EEa

=

0

ε (36)


parameters [Dry89]


ln (37) 0

lnlnEEba +=ε

50



efficiencies


2


Reference source 3


4


between 2 amp 4 5



efficiency

7


51








Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series



40K Series

40K 14608 01066




52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)


53






in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241







54








Mmn = (38)




21

2lnt







equation 310

55

ALMr

C

tB 1461

1461 =ε (310)









56


310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572


57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392


002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)


58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)


59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)


-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)


U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)



60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252


- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )


a = 51057 b = -08147

2 4 6 8 1 0

ln(E)


61










iNC∆ ibC∆




b

iNrel r

C prime=ε (312)


22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62




baE=ε


22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε











are arrived at

63




















64




M(j)

j S S











65



Standard spectrum







66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10


Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)


Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)












sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)










)(iw



70


Let


BB ii ∆=plusmnΒ



22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)



22

∆+

∆=

B

i

A

ii t

BtA

σ (318)


deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71





w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)



02

=partpart


72








0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e


73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)


Energy (keV)


74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)


75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)


76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500


79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000


81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd


82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd








acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured


0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured



85




CCC ∆+= 01 (323)







C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)




2

00

11

2 )()(

part


== CCCxf

Cxfyw kkk

N

kk

N

kkδ


2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86




and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1




and E2 where





Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ



87

Chapter 4




41 WA results





(Bqkg)

Full-energy peak

Absolute efficiency




320 plusmn 5


21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940


88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration


263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940


89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940


90






30 plusmn 14


55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940


91






13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940


92



Nuclide Energies





277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986


93







257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940


94



(Bqkg)


efficiency




52 plusmn 05


46 plusmn 05


95

Nuclide Energies





32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986


96

42 FSA results





Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay





97

Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay




indicated

98









Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand


17A Westonaria sand


6B Kloof mine sand


D6 Brick clay



99





Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand


17A Westonaria Sand


6B Kloof mine Sand


D6 Brick clay











100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S



02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y


W

40K 232Th 238U


101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350


Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932


105

















1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K


5


m p le s

5


a m p le

5


06

m p le s


0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity


232Th


40K



107


uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum









108






232Th


050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA


109

bull Thorium sample















chi-square








110


be omitted [Gar01]























111










112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor






113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)


114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml


115














beaker








Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence




100 timesminus

=full

halffull

TTT

D (41)








117


5

4


2

1 3

Electron












118

CHAPTER 5


51 Outlook





















119












analysis









120

Appendix A





uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B


R = Ap


R = a AP


RR ∆

=∆

R = AP Bq


22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆


121






sum=

=n

iix

nx

1

1 (A1)


(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(






ni xxx 2

n x approaches

m[Deb88]


2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)


122


factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)







ix is 2

ii sw 21=



sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)


sum=

= n

iiw

xs

1

2 1)2( (A6)

123



2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)


124







125


126


0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd


127




teF

t

a micromicro

microminusminus=

1)( (D1)





raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm





D1


int

intΩ

Ω=

d

dl )(θt (D2)



int



Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2


129






beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)


1000

111

259

500

73

159





))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro


ρmicroρmicro

++

+=( (D5)





130


two elements


Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy


(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923


131

Beaker Dimensions


443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm


132



ratios (WAFSA)











133



Singapore (1987)

















134


edition (1997)








(1999)











135








(1979)


New York (2000)


(1988)


Berlin (1987)


(2001)



thesis (2001)

136



















137





Meriden CT 06450 (1998)





unpublished (2002)







138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

Library










short measurements







v

Table of Contents




112 Decay modes3

113 Decay rates5












vi



17 Thesis outline24





213 Electronics28










vii





41 WA Results88

42 FSA Results97





51 Outlook119

APPENDICES






viii


ix

List of Tables


1 m deep 12






calibrations 35









x










by WA method 93









indicated 97

xi



indicated 98



measurement 100





121






xii

LIST OF FIGURES












scale 19



iThemba LABS 26


xiii


detector (B) 28












entrant hole 42





curve

xiv

49

cy

51


calibration 53



















spectrum S 65

xv



















xvi













a fit 85







xvii





















0932) 105

xviii









energy 114









xix

C h a p t e r 1

1 Introduction





















1
























NAZ X



R = R0A13 (11)

2











112 Decay modes





42

42YX A

ZAZ




anti-neutrino


11

10 (13)

3



eA


011 (14)








10

11


(16) eA


minus011









4



(17) eA


minusminus 1

01

113 Decay rates





NdtdN λminus= (18)





λ

2ln21 =t (110)


represented by


5

















way into the earth




and 131I)

6














dN1 = -λ1N1dt (112)



dN2 = (λ1N1 -λ2N2)dt (113)



chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7








t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-





β+

0001




rs

8


45x109

y

117 m



actinium (Ac) 89


francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85


polonium (Po) 84




206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny


9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny


10


























11

















[Van02b]




12

















13








by








γ-ray

Ee

Eγ Nucleus


14

Nucleus

Kα X-ray

γ-ray Electron









given by



photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)











Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ


16














posit


elect511 keV


E

Eγ

ron

ron 511 keV


17



















)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)


target element

18







bull In-situ






19







A

NNN

AN O

O

ff Φbull

Φbull= (120)









being measured






20
















Applied Radiometry



21









Quartz 116 (8) 2 (2) lt 9


Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)


22


























23
















established

17 Thesis outline





24

Chapter 2





















25

211 Physical layout




NIM crate


filling)








26



bull Lead Castle









shown in Appendix C


27


A B







213 Electronics




a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector


data

bull Detector







[USR98]

29




h+

Valence band

Conduction bande-

Eg






30










temperatures




31

bull Detector bias








bull Preamplifiers











bull Amplifier




32
















below


Monitor



33

214 Figure of merit











BchAE += )( ( 21)






follows

(22) CchBchAE ++= )()( 2

34





below

Decay series









35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd


Energy keV

36

energ

y







R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174



37







resolution [Kno79]









38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409















39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI





A ROI C G

30394 511 87 44482









40



high














Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes


067734 28740 1000 0677 Yes


41













42











powder) reference

bull WA






bull FSA





43


method


Mass (kg)

Volume (ml)

Density (gcm3)



232Th FSA IAEA (RGTh) 05157 400 13 3250







24 Data acquisition



software used



44




KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026



Code Elapsed

real time(s)

Elapsed live

time(s)


Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594


28800 28740


116322 116312


45

Chapter 3

Data Analysis




31 Window Analysis



)(EtiB

iN

LMrC

kgBqAε

prime= (31)













46

(32) sum=

=

=ei

siig CC


equation

(33) sum=

=

=ei

siCic CC











ibB

CiNiN C

LL

C

minus=primeC (35)



47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum





48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6










49






b

EEa

=

0

ε (36)


parameters [Dry89]


ln (37) 0

lnlnEEba +=ε

50



efficiencies


2


Reference source 3


4


between 2 amp 4 5



efficiency

7


51








Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series



40K Series

40K 14608 01066




52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)


53






in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241







54








Mmn = (38)




21

2lnt







equation 310

55

ALMr

C

tB 1461

1461 =ε (310)









56


310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572


57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392


002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)


58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)


59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)


-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)


U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)



60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252


- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )


a = 51057 b = -08147

2 4 6 8 1 0

ln(E)


61










iNC∆ ibC∆




b

iNrel r

C prime=ε (312)


22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62




baE=ε


22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε











are arrived at

63




















64




M(j)

j S S











65



Standard spectrum







66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10


Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)


Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)












sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)










)(iw



70


Let


BB ii ∆=plusmnΒ



22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)



22

∆+

∆=

B

i

A

ii t

BtA

σ (318)


deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71





w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)



02

=partpart


72








0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e


73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)


Energy (keV)


74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)


75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)


76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500


79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000


81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd


82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd








acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured


0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured



85




CCC ∆+= 01 (323)







C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)




2

00

11

2 )()(

part


== CCCxf

Cxfyw kkk

N

kk

N

kkδ


2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86




and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1




and E2 where





Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ



87

Chapter 4




41 WA results





(Bqkg)

Full-energy peak

Absolute efficiency




320 plusmn 5


21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940


88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration


263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940


89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940


90






30 plusmn 14


55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940


91






13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940


92



Nuclide Energies





277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986


93







257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940


94



(Bqkg)


efficiency




52 plusmn 05


46 plusmn 05


95

Nuclide Energies





32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986


96

42 FSA results





Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay





97

Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay




indicated

98









Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand


17A Westonaria sand


6B Kloof mine sand


D6 Brick clay



99





Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand


17A Westonaria Sand


6B Kloof mine Sand


D6 Brick clay











100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S



02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y


W

40K 232Th 238U


101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350


Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932


105

















1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K


5


m p le s

5


a m p le

5


06

m p le s


0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity


232Th


40K



107


uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum









108






232Th


050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA


109

bull Thorium sample















chi-square








110


be omitted [Gar01]























111










112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor






113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)


114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml


115














beaker








Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence




100 timesminus

=full

halffull

TTT

D (41)








117


5

4


2

1 3

Electron












118

CHAPTER 5


51 Outlook





















119












analysis









120

Appendix A





uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B


R = Ap


R = a AP


RR ∆

=∆

R = AP Bq


22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆


121






sum=

=n

iix

nx

1

1 (A1)


(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(






ni xxx 2

n x approaches

m[Deb88]


2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)


122


factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)







ix is 2

ii sw 21=



sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)


sum=

= n

iiw

xs

1

2 1)2( (A6)

123



2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)


124







125


126


0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd


127




teF

t

a micromicro

microminusminus=

1)( (D1)





raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm





D1


int

intΩ

Ω=

d

dl )(θt (D2)



int



Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2


129






beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)


1000

111

259

500

73

159





))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro


ρmicroρmicro

++

+=( (D5)





130


two elements


Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy


(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923


131

Beaker Dimensions


443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm


132



ratios (WAFSA)











133



Singapore (1987)

















134


edition (1997)








(1999)











135








(1979)


New York (2000)


(1988)


Berlin (1987)


(2001)



thesis (2001)

136



















137





Meriden CT 06450 (1998)





unpublished (2002)







138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

Library


Table of Contents




112 Decay modes3

113 Decay rates5












vi



17 Thesis outline24





213 Electronics28










vii





41 WA Results88

42 FSA Results97





51 Outlook119

APPENDICES






viii


ix

List of Tables


1 m deep 12






calibrations 35









x










by WA method 93









indicated 97

xi



indicated 98



measurement 100





121






xii

LIST OF FIGURES












scale 19



iThemba LABS 26


xiii


detector (B) 28












entrant hole 42





curve

xiv

49

cy

51


calibration 53



















spectrum S 65

xv



















xvi













a fit 85







xvii





















0932) 105

xviii









energy 114









xix

C h a p t e r 1

1 Introduction





















1
























NAZ X



R = R0A13 (11)

2











112 Decay modes





42

42YX A

ZAZ




anti-neutrino


11

10 (13)

3



eA


011 (14)








10

11


(16) eA


minus011









4



(17) eA


minusminus 1

01

113 Decay rates





NdtdN λminus= (18)





λ

2ln21 =t (110)


represented by


5

















way into the earth




and 131I)

6














dN1 = -λ1N1dt (112)



dN2 = (λ1N1 -λ2N2)dt (113)



chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7








t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-





β+

0001




rs

8


45x109

y

117 m



actinium (Ac) 89


francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85


polonium (Po) 84




206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny


9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny


10


























11

















[Van02b]




12

















13








by








γ-ray

Ee

Eγ Nucleus


14

Nucleus

Kα X-ray

γ-ray Electron









given by



photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)











Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ


16














posit


elect511 keV


E

Eγ

ron

ron 511 keV


17



















)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)


target element

18







bull In-situ






19







A

NNN

AN O

O

ff Φbull

Φbull= (120)









being measured






20
















Applied Radiometry



21









Quartz 116 (8) 2 (2) lt 9


Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)


22


























23
















established

17 Thesis outline





24

Chapter 2





















25

211 Physical layout




NIM crate


filling)








26



bull Lead Castle









shown in Appendix C


27


A B







213 Electronics




a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector


data

bull Detector







[USR98]

29




h+

Valence band

Conduction bande-

Eg






30










temperatures




31

bull Detector bias








bull Preamplifiers











bull Amplifier




32
















below


Monitor



33

214 Figure of merit











BchAE += )( ( 21)






follows

(22) CchBchAE ++= )()( 2

34





below

Decay series









35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd


Energy keV

36

energ

y







R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174



37







resolution [Kno79]









38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409















39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI





A ROI C G

30394 511 87 44482









40



high














Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes


067734 28740 1000 0677 Yes


41













42











powder) reference

bull WA






bull FSA





43


method


Mass (kg)

Volume (ml)

Density (gcm3)



232Th FSA IAEA (RGTh) 05157 400 13 3250







24 Data acquisition



software used



44




KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026



Code Elapsed

real time(s)

Elapsed live

time(s)


Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594


28800 28740


116322 116312


45

Chapter 3

Data Analysis




31 Window Analysis



)(EtiB

iN

LMrC

kgBqAε

prime= (31)













46

(32) sum=

=

=ei

siig CC


equation

(33) sum=

=

=ei

siCic CC











ibB

CiNiN C

LL

C

minus=primeC (35)



47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum





48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6










49






b

EEa

=

0

ε (36)


parameters [Dry89]


ln (37) 0

lnlnEEba +=ε

50



efficiencies


2


Reference source 3


4


between 2 amp 4 5



efficiency

7


51








Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series



40K Series

40K 14608 01066




52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)


53






in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241







54








Mmn = (38)




21

2lnt







equation 310

55

ALMr

C

tB 1461

1461 =ε (310)









56


310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572


57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392


002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)


58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)


59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)


-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)


U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)



60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252


- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )


a = 51057 b = -08147

2 4 6 8 1 0

ln(E)


61










iNC∆ ibC∆




b

iNrel r

C prime=ε (312)


22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62




baE=ε


22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε











are arrived at

63




















64




M(j)

j S S











65



Standard spectrum







66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10


Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)


Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)












sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)










)(iw



70


Let


BB ii ∆=plusmnΒ



22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)



22

∆+

∆=

B

i

A

ii t

BtA

σ (318)


deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71





w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)



02

=partpart


72








0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e


73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)


Energy (keV)


74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)


75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)


76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500


79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000


81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd


82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd








acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured


0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured



85




CCC ∆+= 01 (323)







C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)




2

00

11

2 )()(

part


== CCCxf

Cxfyw kkk

N

kk

N

kkδ


2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86




and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1




and E2 where





Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ



87

Chapter 4




41 WA results





(Bqkg)

Full-energy peak

Absolute efficiency




320 plusmn 5


21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940


88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration


263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940


89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940


90






30 plusmn 14


55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940


91






13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940


92



Nuclide Energies





277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986


93







257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940


94



(Bqkg)


efficiency




52 plusmn 05


46 plusmn 05


95

Nuclide Energies





32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986


96

42 FSA results





Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay





97

Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay




indicated

98









Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand


17A Westonaria sand


6B Kloof mine sand


D6 Brick clay



99





Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand


17A Westonaria Sand


6B Kloof mine Sand


D6 Brick clay











100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S



02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y


W

40K 232Th 238U


101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350


Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932


105

















1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K


5


m p le s

5


a m p le

5


06

m p le s


0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity


232Th


40K



107


uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum









108






232Th


050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA


109

bull Thorium sample















chi-square








110


be omitted [Gar01]























111










112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor






113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)


114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml


115














beaker








Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence




100 timesminus

=full

halffull

TTT

D (41)








117


5

4


2

1 3

Electron












118

CHAPTER 5


51 Outlook





















119












analysis









120

Appendix A





uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B


R = Ap


R = a AP


RR ∆

=∆

R = AP Bq


22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆


121






sum=

=n

iix

nx

1

1 (A1)


(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(






ni xxx 2

n x approaches

m[Deb88]


2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)


122


factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)







ix is 2

ii sw 21=



sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)


sum=

= n

iiw

xs

1

2 1)2( (A6)

123



2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)


124







125


126


0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd


127




teF

t

a micromicro

microminusminus=

1)( (D1)





raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm





D1


int

intΩ

Ω=

d

dl )(θt (D2)



int



Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2


129






beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)


1000

111

259

500

73

159





))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro


ρmicroρmicro

++

+=( (D5)





130


two elements


Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy


(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923


131

Beaker Dimensions


443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm


132



ratios (WAFSA)











133



Singapore (1987)

















134


edition (1997)








(1999)











135








(1979)


New York (2000)


(1988)


Berlin (1987)


(2001)



thesis (2001)

136



















137





Meriden CT 06450 (1998)





unpublished (2002)







138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

Library




17 Thesis outline24





213 Electronics28










vii





41 WA Results88

42 FSA Results97





51 Outlook119

APPENDICES






viii


ix

List of Tables


1 m deep 12






calibrations 35









x










by WA method 93









indicated 97

xi



indicated 98



measurement 100





121






xii

LIST OF FIGURES












scale 19



iThemba LABS 26


xiii


detector (B) 28












entrant hole 42





curve

xiv

49

cy

51


calibration 53



















spectrum S 65

xv



















xvi













a fit 85







xvii





















0932) 105

xviii









energy 114









xix

C h a p t e r 1

1 Introduction





















1
























NAZ X



R = R0A13 (11)

2











112 Decay modes





42

42YX A

ZAZ




anti-neutrino


11

10 (13)

3



eA


011 (14)








10

11


(16) eA


minus011









4



(17) eA


minusminus 1

01

113 Decay rates





NdtdN λminus= (18)





λ

2ln21 =t (110)


represented by


5

















way into the earth




and 131I)

6














dN1 = -λ1N1dt (112)



dN2 = (λ1N1 -λ2N2)dt (113)



chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7








t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-





β+

0001




rs

8


45x109

y

117 m



actinium (Ac) 89


francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85


polonium (Po) 84




206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny


9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny


10


























11

















[Van02b]




12

















13








by








γ-ray

Ee

Eγ Nucleus


14

Nucleus

Kα X-ray

γ-ray Electron









given by



photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)











Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ


16














posit


elect511 keV


E

Eγ

ron

ron 511 keV


17



















)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)


target element

18







bull In-situ






19







A

NNN

AN O

O

ff Φbull

Φbull= (120)









being measured






20
















Applied Radiometry



21









Quartz 116 (8) 2 (2) lt 9


Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)


22


























23
















established

17 Thesis outline





24

Chapter 2





















25

211 Physical layout




NIM crate


filling)








26



bull Lead Castle









shown in Appendix C


27


A B







213 Electronics




a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector


data

bull Detector







[USR98]

29




h+

Valence band

Conduction bande-

Eg






30










temperatures




31

bull Detector bias








bull Preamplifiers











bull Amplifier




32
















below


Monitor



33

214 Figure of merit











BchAE += )( ( 21)






follows

(22) CchBchAE ++= )()( 2

34





below

Decay series









35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd


Energy keV

36

energ

y







R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174



37







resolution [Kno79]









38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409















39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI





A ROI C G

30394 511 87 44482









40



high














Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes


067734 28740 1000 0677 Yes


41













42











powder) reference

bull WA






bull FSA





43


method


Mass (kg)

Volume (ml)

Density (gcm3)



232Th FSA IAEA (RGTh) 05157 400 13 3250







24 Data acquisition



software used



44




KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026



Code Elapsed

real time(s)

Elapsed live

time(s)


Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594


28800 28740


116322 116312


45

Chapter 3

Data Analysis




31 Window Analysis



)(EtiB

iN

LMrC

kgBqAε

prime= (31)













46

(32) sum=

=

=ei

siig CC


equation

(33) sum=

=

=ei

siCic CC











ibB

CiNiN C

LL

C

minus=primeC (35)



47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum





48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6










49






b

EEa

=

0

ε (36)


parameters [Dry89]


ln (37) 0

lnlnEEba +=ε

50



efficiencies


2


Reference source 3


4


between 2 amp 4 5



efficiency

7


51








Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series



40K Series

40K 14608 01066




52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)


53






in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241







54








Mmn = (38)




21

2lnt







equation 310

55

ALMr

C

tB 1461

1461 =ε (310)









56


310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572


57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392


002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)


58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)


59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)


-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)


U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)



60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252


- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )


a = 51057 b = -08147

2 4 6 8 1 0

ln(E)


61










iNC∆ ibC∆




b

iNrel r

C prime=ε (312)


22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62




baE=ε


22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε











are arrived at

63




















64




M(j)

j S S











65



Standard spectrum







66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10


Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)


Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)












sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)










)(iw



70


Let


BB ii ∆=plusmnΒ



22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)



22

∆+

∆=

B

i

A

ii t

BtA

σ (318)


deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71





w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)



02

=partpart


72








0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e


73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)


Energy (keV)


74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)


75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)


76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500


79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000


81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd


82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd








acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured


0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured



85




CCC ∆+= 01 (323)







C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)




2

00

11

2 )()(

part


== CCCxf

Cxfyw kkk

N

kk

N

kkδ


2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86




and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1




and E2 where





Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ



87

Chapter 4




41 WA results





(Bqkg)

Full-energy peak

Absolute efficiency




320 plusmn 5


21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940


88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration


263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940


89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940


90






30 plusmn 14


55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940


91






13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940


92



Nuclide Energies





277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986


93







257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940


94



(Bqkg)


efficiency




52 plusmn 05


46 plusmn 05


95

Nuclide Energies





32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986


96

42 FSA results





Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay





97

Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay




indicated

98









Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand


17A Westonaria sand


6B Kloof mine sand


D6 Brick clay



99





Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand


17A Westonaria Sand


6B Kloof mine Sand


D6 Brick clay











100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S



02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y


W

40K 232Th 238U


101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350


Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932


105

















1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K


5


m p le s

5


a m p le

5


06

m p le s


0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity


232Th


40K



107


uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum









108






232Th


050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA


109

bull Thorium sample















chi-square








110


be omitted [Gar01]























111










112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor






113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)


114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml


115














beaker








Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence




100 timesminus

=full

halffull

TTT

D (41)








117


5

4


2

1 3

Electron












118

CHAPTER 5


51 Outlook





















119












analysis









120

Appendix A





uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B


R = Ap


R = a AP


RR ∆

=∆

R = AP Bq


22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆


121






sum=

=n

iix

nx

1

1 (A1)


(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(






ni xxx 2

n x approaches

m[Deb88]


2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)


122


factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)







ix is 2

ii sw 21=



sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)


sum=

= n

iiw

xs

1

2 1)2( (A6)

123



2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)


124







125


126


0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd


127




teF

t

a micromicro

microminusminus=

1)( (D1)





raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm





D1


int

intΩ

Ω=

d

dl )(θt (D2)



int



Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2


129






beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)


1000

111

259

500

73

159





))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro


ρmicroρmicro

++

+=( (D5)





130


two elements


Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy


(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923


131

Beaker Dimensions


443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm


132



ratios (WAFSA)











133



Singapore (1987)

















134


edition (1997)








(1999)











135








(1979)


New York (2000)


(1988)


Berlin (1987)


(2001)



thesis (2001)

136



















137





Meriden CT 06450 (1998)





unpublished (2002)







138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

Library






41 WA Results88

42 FSA Results97





51 Outlook119

APPENDICES






viii


ix

List of Tables


1 m deep 12






calibrations 35









x










by WA method 93









indicated 97

xi



indicated 98



measurement 100





121






xii

LIST OF FIGURES












scale 19



iThemba LABS 26


xiii


detector (B) 28












entrant hole 42





curve

xiv

49

cy

51


calibration 53



















spectrum S 65

xv



















xvi













a fit 85







xvii





















0932) 105

xviii









energy 114









xix

C h a p t e r 1

1 Introduction





















1
























NAZ X



R = R0A13 (11)

2











112 Decay modes





42

42YX A

ZAZ




anti-neutrino


11

10 (13)

3



eA


011 (14)








10

11


(16) eA


minus011









4



(17) eA


minusminus 1

01

113 Decay rates





NdtdN λminus= (18)





λ

2ln21 =t (110)


represented by


5

















way into the earth




and 131I)

6














dN1 = -λ1N1dt (112)



dN2 = (λ1N1 -λ2N2)dt (113)



chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7








t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-





β+

0001




rs

8


45x109

y

117 m



actinium (Ac) 89


francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85


polonium (Po) 84




206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny


9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny


10


























11

















[Van02b]




12

















13








by








γ-ray

Ee

Eγ Nucleus


14

Nucleus

Kα X-ray

γ-ray Electron









given by



photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)











Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ


16














posit


elect511 keV


E

Eγ

ron

ron 511 keV


17



















)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)


target element

18







bull In-situ






19







A

NNN

AN O

O

ff Φbull

Φbull= (120)









being measured






20
















Applied Radiometry



21









Quartz 116 (8) 2 (2) lt 9


Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)


22


























23
















established

17 Thesis outline





24

Chapter 2





















25

211 Physical layout




NIM crate


filling)








26



bull Lead Castle









shown in Appendix C


27


A B







213 Electronics




a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector


data

bull Detector







[USR98]

29




h+

Valence band

Conduction bande-

Eg






30










temperatures




31

bull Detector bias








bull Preamplifiers











bull Amplifier




32
















below


Monitor



33

214 Figure of merit











BchAE += )( ( 21)






follows

(22) CchBchAE ++= )()( 2

34





below

Decay series









35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd


Energy keV

36

energ

y







R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174



37







resolution [Kno79]









38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409















39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI





A ROI C G

30394 511 87 44482









40



high














Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes


067734 28740 1000 0677 Yes


41













42











powder) reference

bull WA






bull FSA





43


method


Mass (kg)

Volume (ml)

Density (gcm3)



232Th FSA IAEA (RGTh) 05157 400 13 3250







24 Data acquisition



software used



44




KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026



Code Elapsed

real time(s)

Elapsed live

time(s)


Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594


28800 28740


116322 116312


45

Chapter 3

Data Analysis




31 Window Analysis



)(EtiB

iN

LMrC

kgBqAε

prime= (31)













46

(32) sum=

=

=ei

siig CC


equation

(33) sum=

=

=ei

siCic CC











ibB

CiNiN C

LL

C

minus=primeC (35)



47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum





48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6










49






b

EEa

=

0

ε (36)


parameters [Dry89]


ln (37) 0

lnlnEEba +=ε

50



efficiencies


2


Reference source 3


4


between 2 amp 4 5



efficiency

7


51








Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series



40K Series

40K 14608 01066




52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)


53






in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241







54








Mmn = (38)




21

2lnt







equation 310

55

ALMr

C

tB 1461

1461 =ε (310)









56


310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572


57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392


002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)


58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)


59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)


-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)


U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)



60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252


- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )


a = 51057 b = -08147

2 4 6 8 1 0

ln(E)


61










iNC∆ ibC∆




b

iNrel r

C prime=ε (312)


22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62




baE=ε


22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε











are arrived at

63




















64




M(j)

j S S











65



Standard spectrum







66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10


Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)


Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)












sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)










)(iw



70


Let


BB ii ∆=plusmnΒ



22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)



22

∆+

∆=

B

i

A

ii t

BtA

σ (318)


deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71





w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)



02

=partpart


72








0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e


73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)


Energy (keV)


74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)


75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)


76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500


79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000


81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd


82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd








acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured


0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured



85




CCC ∆+= 01 (323)







C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)




2

00

11

2 )()(

part


== CCCxf

Cxfyw kkk

N

kk

N

kkδ


2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86




and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1




and E2 where





Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ



87

Chapter 4




41 WA results





(Bqkg)

Full-energy peak

Absolute efficiency




320 plusmn 5


21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940


88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration


263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940


89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940


90






30 plusmn 14


55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940


91






13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940


92



Nuclide Energies





277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986


93







257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940


94



(Bqkg)


efficiency




52 plusmn 05


46 plusmn 05


95

Nuclide Energies





32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986


96

42 FSA results





Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay





97

Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay




indicated

98









Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand


17A Westonaria sand


6B Kloof mine sand


D6 Brick clay



99





Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand


17A Westonaria Sand


6B Kloof mine Sand


D6 Brick clay











100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S



02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y


W

40K 232Th 238U


101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350


Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932


105

















1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K


5


m p le s

5


a m p le

5


06

m p le s


0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity


232Th


40K



107


uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum









108






232Th


050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA


109

bull Thorium sample















chi-square








110


be omitted [Gar01]























111










112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor






113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)


114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml


115














beaker








Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence




100 timesminus

=full

halffull

TTT

D (41)








117


5

4


2

1 3

Electron












118

CHAPTER 5


51 Outlook





















119












analysis









120

Appendix A





uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B


R = Ap


R = a AP


RR ∆

=∆

R = AP Bq


22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆


121






sum=

=n

iix

nx

1

1 (A1)


(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(






ni xxx 2

n x approaches

m[Deb88]


2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)


122


factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)







ix is 2

ii sw 21=



sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)


sum=

= n

iiw

xs

1

2 1)2( (A6)

123



2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)


124







125


126


0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd


127




teF

t

a micromicro

microminusminus=

1)( (D1)





raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm





D1


int

intΩ

Ω=

d

dl )(θt (D2)



int



Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2


129






beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)


1000

111

259

500

73

159





))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro


ρmicroρmicro

++

+=( (D5)





130


two elements


Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy


(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923


131

Beaker Dimensions


443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm


132



ratios (WAFSA)











133



Singapore (1987)

















134


edition (1997)








(1999)











135








(1979)


New York (2000)


(1988)


Berlin (1987)


(2001)



thesis (2001)

136



















137





Meriden CT 06450 (1998)





unpublished (2002)







138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

Library



ix

List of Tables


1 m deep 12






calibrations 35









x










by WA method 93









indicated 97

xi



indicated 98



measurement 100





121






xii

LIST OF FIGURES












scale 19



iThemba LABS 26


xiii


detector (B) 28












entrant hole 42





curve

xiv

49

cy

51


calibration 53



















spectrum S 65

xv



















xvi













a fit 85







xvii





















0932) 105

xviii









energy 114









xix

C h a p t e r 1

1 Introduction





















1
























NAZ X



R = R0A13 (11)

2











112 Decay modes





42

42YX A

ZAZ




anti-neutrino


11

10 (13)

3



eA


011 (14)








10

11


(16) eA


minus011









4



(17) eA


minusminus 1

01

113 Decay rates





NdtdN λminus= (18)





λ

2ln21 =t (110)


represented by


5

















way into the earth




and 131I)

6














dN1 = -λ1N1dt (112)



dN2 = (λ1N1 -λ2N2)dt (113)



chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7








t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-





β+

0001




rs

8


45x109

y

117 m



actinium (Ac) 89


francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85


polonium (Po) 84




206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny


9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny


10


























11

















[Van02b]




12

















13








by








γ-ray

Ee

Eγ Nucleus


14

Nucleus

Kα X-ray

γ-ray Electron









given by



photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)











Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ


16














posit


elect511 keV


E

Eγ

ron

ron 511 keV


17



















)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)


target element

18







bull In-situ






19







A

NNN

AN O

O

ff Φbull

Φbull= (120)









being measured






20
















Applied Radiometry



21









Quartz 116 (8) 2 (2) lt 9


Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)


22


























23
















established

17 Thesis outline





24

Chapter 2





















25

211 Physical layout




NIM crate


filling)








26



bull Lead Castle









shown in Appendix C


27


A B







213 Electronics




a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector


data

bull Detector







[USR98]

29




h+

Valence band

Conduction bande-

Eg






30










temperatures




31

bull Detector bias








bull Preamplifiers











bull Amplifier




32
















below


Monitor



33

214 Figure of merit











BchAE += )( ( 21)






follows

(22) CchBchAE ++= )()( 2

34





below

Decay series









35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd


Energy keV

36

energ

y







R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174



37







resolution [Kno79]









38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409















39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI





A ROI C G

30394 511 87 44482









40



high














Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes


067734 28740 1000 0677 Yes


41













42











powder) reference

bull WA






bull FSA





43


method


Mass (kg)

Volume (ml)

Density (gcm3)



232Th FSA IAEA (RGTh) 05157 400 13 3250







24 Data acquisition



software used



44




KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026



Code Elapsed

real time(s)

Elapsed live

time(s)


Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594


28800 28740


116322 116312


45

Chapter 3

Data Analysis




31 Window Analysis



)(EtiB

iN

LMrC

kgBqAε

prime= (31)













46

(32) sum=

=

=ei

siig CC


equation

(33) sum=

=

=ei

siCic CC











ibB

CiNiN C

LL

C

minus=primeC (35)



47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum





48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6










49






b

EEa

=

0

ε (36)


parameters [Dry89]


ln (37) 0

lnlnEEba +=ε

50



efficiencies


2


Reference source 3


4


between 2 amp 4 5



efficiency

7


51








Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series



40K Series

40K 14608 01066




52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)


53






in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241







54








Mmn = (38)




21

2lnt







equation 310

55

ALMr

C

tB 1461

1461 =ε (310)









56


310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572


57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392


002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)


58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)


59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)


-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)


U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)



60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252


- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )


a = 51057 b = -08147

2 4 6 8 1 0

ln(E)


61










iNC∆ ibC∆




b

iNrel r

C prime=ε (312)


22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62




baE=ε


22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε











are arrived at

63




















64




M(j)

j S S











65



Standard spectrum







66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10


Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)


Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)












sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)










)(iw



70


Let


BB ii ∆=plusmnΒ



22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)



22

∆+

∆=

B

i

A

ii t

BtA

σ (318)


deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71





w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)



02

=partpart


72








0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e


73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)


Energy (keV)


74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)


75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)


76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500


79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000


81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd


82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd








acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured


0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured



85




CCC ∆+= 01 (323)







C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)




2

00

11

2 )()(

part


== CCCxf

Cxfyw kkk

N

kk

N

kkδ


2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86




and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1




and E2 where





Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ



87

Chapter 4




41 WA results





(Bqkg)

Full-energy peak

Absolute efficiency




320 plusmn 5


21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940


88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration


263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940


89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940


90






30 plusmn 14


55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940


91






13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940


92



Nuclide Energies





277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986


93







257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940


94



(Bqkg)


efficiency




52 plusmn 05


46 plusmn 05


95

Nuclide Energies





32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986


96

42 FSA results





Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay





97

Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay




indicated

98









Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand


17A Westonaria sand


6B Kloof mine sand


D6 Brick clay



99





Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand


17A Westonaria Sand


6B Kloof mine Sand


D6 Brick clay











100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S



02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y


W

40K 232Th 238U


101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350


Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932


105

















1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K


5


m p le s

5


a m p le

5


06

m p le s


0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity


232Th


40K



107


uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum









108






232Th


050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA


109

bull Thorium sample















chi-square








110


be omitted [Gar01]























111










112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor






113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)


114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml


115














beaker








Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence




100 timesminus

=full

halffull

TTT

D (41)








117


5

4


2

1 3

Electron












118

CHAPTER 5


51 Outlook





















119












analysis









120

Appendix A





uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B


R = Ap


R = a AP


RR ∆

=∆

R = AP Bq


22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆


121






sum=

=n

iix

nx

1

1 (A1)


(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(






ni xxx 2

n x approaches

m[Deb88]


2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)


122


factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)







ix is 2

ii sw 21=



sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)


sum=

= n

iiw

xs

1

2 1)2( (A6)

123



2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)


124







125


126


0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd


127




teF

t

a micromicro

microminusminus=

1)( (D1)





raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm





D1


int

intΩ

Ω=

d

dl )(θt (D2)



int



Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2


129






beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)


1000

111

259

500

73

159





))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro


ρmicroρmicro

++

+=( (D5)





130


two elements


Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy


(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923


131

Beaker Dimensions


443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm


132



ratios (WAFSA)











133



Singapore (1987)

















134


edition (1997)








(1999)











135








(1979)


New York (2000)


(1988)


Berlin (1987)


(2001)



thesis (2001)

136



















137





Meriden CT 06450 (1998)





unpublished (2002)







138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

Library


List of Tables


1 m deep 12






calibrations 35









x










by WA method 93









indicated 97

xi



indicated 98



measurement 100





121






xii

LIST OF FIGURES












scale 19



iThemba LABS 26


xiii


detector (B) 28












entrant hole 42





curve

xiv

49

cy

51


calibration 53



















spectrum S 65

xv



















xvi













a fit 85







xvii





















0932) 105

xviii









energy 114









xix

C h a p t e r 1

1 Introduction





















1
























NAZ X



R = R0A13 (11)

2











112 Decay modes





42

42YX A

ZAZ




anti-neutrino


11

10 (13)

3



eA


011 (14)








10

11


(16) eA


minus011









4



(17) eA


minusminus 1

01

113 Decay rates





NdtdN λminus= (18)





λ

2ln21 =t (110)


represented by


5

















way into the earth




and 131I)

6














dN1 = -λ1N1dt (112)



dN2 = (λ1N1 -λ2N2)dt (113)



chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7








t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-





β+

0001




rs

8


45x109

y

117 m



actinium (Ac) 89


francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85


polonium (Po) 84




206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny


9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny


10


























11

















[Van02b]




12

















13








by








γ-ray

Ee

Eγ Nucleus


14

Nucleus

Kα X-ray

γ-ray Electron









given by



photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)











Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ


16














posit


elect511 keV


E

Eγ

ron

ron 511 keV


17



















)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)


target element

18







bull In-situ






19







A

NNN

AN O

O

ff Φbull

Φbull= (120)









being measured






20
















Applied Radiometry



21









Quartz 116 (8) 2 (2) lt 9


Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)


22


























23
















established

17 Thesis outline





24

Chapter 2





















25

211 Physical layout




NIM crate


filling)








26



bull Lead Castle









shown in Appendix C


27


A B







213 Electronics




a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector


data

bull Detector







[USR98]

29




h+

Valence band

Conduction bande-

Eg






30










temperatures




31

bull Detector bias








bull Preamplifiers











bull Amplifier




32
















below


Monitor



33

214 Figure of merit











BchAE += )( ( 21)






follows

(22) CchBchAE ++= )()( 2

34





below

Decay series









35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd


Energy keV

36

energ

y







R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174



37







resolution [Kno79]









38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409















39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI





A ROI C G

30394 511 87 44482









40



high














Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes


067734 28740 1000 0677 Yes


41













42











powder) reference

bull WA






bull FSA





43


method


Mass (kg)

Volume (ml)

Density (gcm3)



232Th FSA IAEA (RGTh) 05157 400 13 3250







24 Data acquisition



software used



44




KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026



Code Elapsed

real time(s)

Elapsed live

time(s)


Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594


28800 28740


116322 116312


45

Chapter 3

Data Analysis




31 Window Analysis



)(EtiB

iN

LMrC

kgBqAε

prime= (31)













46

(32) sum=

=

=ei

siig CC


equation

(33) sum=

=

=ei

siCic CC











ibB

CiNiN C

LL

C

minus=primeC (35)



47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum





48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6










49






b

EEa

=

0

ε (36)


parameters [Dry89]


ln (37) 0

lnlnEEba +=ε

50



efficiencies


2


Reference source 3


4


between 2 amp 4 5



efficiency

7


51








Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series



40K Series

40K 14608 01066




52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)


53






in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241







54








Mmn = (38)




21

2lnt







equation 310

55

ALMr

C

tB 1461

1461 =ε (310)









56


310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572


57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392


002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)


58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)


59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)


-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)


U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)



60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252


- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )


a = 51057 b = -08147

2 4 6 8 1 0

ln(E)


61










iNC∆ ibC∆




b

iNrel r

C prime=ε (312)


22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62




baE=ε


22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε











are arrived at

63




















64




M(j)

j S S











65



Standard spectrum







66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10


Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)


Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)












sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)










)(iw



70


Let


BB ii ∆=plusmnΒ



22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)



22

∆+

∆=

B

i

A

ii t

BtA

σ (318)


deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71





w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)



02

=partpart


72








0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e


73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)


Energy (keV)


74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)


75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)


76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500


79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000


81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd


82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd








acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured


0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured



85




CCC ∆+= 01 (323)







C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)




2

00

11

2 )()(

part


== CCCxf

Cxfyw kkk

N

kk

N

kkδ


2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86




and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1




and E2 where





Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ



87

Chapter 4




41 WA results





(Bqkg)

Full-energy peak

Absolute efficiency




320 plusmn 5


21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940


88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration


263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940


89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940


90






30 plusmn 14


55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940


91






13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940


92



Nuclide Energies





277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986


93







257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940


94



(Bqkg)


efficiency




52 plusmn 05


46 plusmn 05


95

Nuclide Energies





32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986


96

42 FSA results





Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay





97

Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay




indicated

98









Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand


17A Westonaria sand


6B Kloof mine sand


D6 Brick clay



99





Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand


17A Westonaria Sand


6B Kloof mine Sand


D6 Brick clay











100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S



02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y


W

40K 232Th 238U


101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350


Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932


105

















1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K


5


m p le s

5


a m p le

5


06

m p le s


0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity


232Th


40K



107


uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum









108






232Th


050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA


109

bull Thorium sample















chi-square








110


be omitted [Gar01]























111










112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor






113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)


114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml


115














beaker








Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence




100 timesminus

=full

halffull

TTT

D (41)








117


5

4


2

1 3

Electron












118

CHAPTER 5


51 Outlook





















119












analysis









120

Appendix A





uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B


R = Ap


R = a AP


RR ∆

=∆

R = AP Bq


22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆


121






sum=

=n

iix

nx

1

1 (A1)


(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(






ni xxx 2

n x approaches

m[Deb88]


2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)


122


factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)







ix is 2

ii sw 21=



sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)


sum=

= n

iiw

xs

1

2 1)2( (A6)

123



2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)


124







125


126


0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd


127




teF

t

a micromicro

microminusminus=

1)( (D1)





raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm





D1


int

intΩ

Ω=

d

dl )(θt (D2)



int



Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2


129






beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)


1000

111

259

500

73

159





))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro


ρmicroρmicro

++

+=( (D5)





130


two elements


Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy


(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923


131

Beaker Dimensions


443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm


132



ratios (WAFSA)











133



Singapore (1987)

















134


edition (1997)








(1999)











135








(1979)


New York (2000)


(1988)


Berlin (1987)


(2001)



thesis (2001)

136



















137





Meriden CT 06450 (1998)





unpublished (2002)







138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

Library











by WA method 93









indicated 97

xi



indicated 98



measurement 100





121






xii

LIST OF FIGURES












scale 19



iThemba LABS 26


xiii


detector (B) 28












entrant hole 42





curve

xiv

49

cy

51


calibration 53



















spectrum S 65

xv



















xvi













a fit 85







xvii





















0932) 105

xviii









energy 114









xix

C h a p t e r 1

1 Introduction





















1
























NAZ X



R = R0A13 (11)

2











112 Decay modes





42

42YX A

ZAZ




anti-neutrino


11

10 (13)

3



eA


011 (14)








10

11


(16) eA


minus011









4



(17) eA


minusminus 1

01

113 Decay rates





NdtdN λminus= (18)





λ

2ln21 =t (110)


represented by


5

















way into the earth




and 131I)

6














dN1 = -λ1N1dt (112)



dN2 = (λ1N1 -λ2N2)dt (113)



chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7








t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-





β+

0001




rs

8


45x109

y

117 m



actinium (Ac) 89


francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85


polonium (Po) 84




206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny


9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny


10


























11

















[Van02b]




12

















13








by








γ-ray

Ee

Eγ Nucleus


14

Nucleus

Kα X-ray

γ-ray Electron









given by



photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)











Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ


16














posit


elect511 keV


E

Eγ

ron

ron 511 keV


17



















)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)


target element

18







bull In-situ






19







A

NNN

AN O

O

ff Φbull

Φbull= (120)









being measured






20
















Applied Radiometry



21









Quartz 116 (8) 2 (2) lt 9


Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)


22


























23
















established

17 Thesis outline





24

Chapter 2





















25

211 Physical layout




NIM crate


filling)








26



bull Lead Castle









shown in Appendix C


27


A B







213 Electronics




a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector


data

bull Detector







[USR98]

29




h+

Valence band

Conduction bande-

Eg






30










temperatures




31

bull Detector bias








bull Preamplifiers











bull Amplifier




32
















below


Monitor



33

214 Figure of merit











BchAE += )( ( 21)






follows

(22) CchBchAE ++= )()( 2

34





below

Decay series









35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd


Energy keV

36

energ

y







R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174



37







resolution [Kno79]









38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409















39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI





A ROI C G

30394 511 87 44482









40



high














Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes


067734 28740 1000 0677 Yes


41













42











powder) reference

bull WA






bull FSA





43


method


Mass (kg)

Volume (ml)

Density (gcm3)



232Th FSA IAEA (RGTh) 05157 400 13 3250







24 Data acquisition



software used



44




KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026



Code Elapsed

real time(s)

Elapsed live

time(s)


Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594


28800 28740


116322 116312


45

Chapter 3

Data Analysis




31 Window Analysis



)(EtiB

iN

LMrC

kgBqAε

prime= (31)













46

(32) sum=

=

=ei

siig CC


equation

(33) sum=

=

=ei

siCic CC











ibB

CiNiN C

LL

C

minus=primeC (35)



47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum





48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6










49






b

EEa

=

0

ε (36)


parameters [Dry89]


ln (37) 0

lnlnEEba +=ε

50



efficiencies


2


Reference source 3


4


between 2 amp 4 5



efficiency

7


51








Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series



40K Series

40K 14608 01066




52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)


53






in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241







54








Mmn = (38)




21

2lnt







equation 310

55

ALMr

C

tB 1461

1461 =ε (310)









56


310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572


57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392


002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)


58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)


59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)


-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)


U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)



60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252


- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )


a = 51057 b = -08147

2 4 6 8 1 0

ln(E)


61










iNC∆ ibC∆




b

iNrel r

C prime=ε (312)


22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62




baE=ε


22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε











are arrived at

63




















64




M(j)

j S S











65



Standard spectrum







66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10


Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)


Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)












sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)










)(iw



70


Let


BB ii ∆=plusmnΒ



22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)



22

∆+

∆=

B

i

A

ii t

BtA

σ (318)


deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71





w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)



02

=partpart


72








0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e


73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)


Energy (keV)


74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)


75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)


76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500


79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000


81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd


82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd








acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured


0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured



85




CCC ∆+= 01 (323)







C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)




2

00

11

2 )()(

part


== CCCxf

Cxfyw kkk

N

kk

N

kkδ


2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86




and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1




and E2 where





Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ



87

Chapter 4




41 WA results





(Bqkg)

Full-energy peak

Absolute efficiency




320 plusmn 5


21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940


88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration


263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940


89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940


90






30 plusmn 14


55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940


91






13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940


92



Nuclide Energies





277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986


93







257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940


94



(Bqkg)


efficiency




52 plusmn 05


46 plusmn 05


95

Nuclide Energies





32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986


96

42 FSA results





Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay





97

Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay




indicated

98









Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand


17A Westonaria sand


6B Kloof mine sand


D6 Brick clay



99





Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand


17A Westonaria Sand


6B Kloof mine Sand


D6 Brick clay











100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S



02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y


W

40K 232Th 238U


101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350


Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932


105

















1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K


5


m p le s

5


a m p le

5


06

m p le s


0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity


232Th


40K



107


uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum









108






232Th


050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA


109

bull Thorium sample















chi-square








110


be omitted [Gar01]























111










112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor






113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)


114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml


115














beaker








Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence




100 timesminus

=full

halffull

TTT

D (41)








117


5

4


2

1 3

Electron












118

CHAPTER 5


51 Outlook





















119












analysis









120

Appendix A





uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B


R = Ap


R = a AP


RR ∆

=∆

R = AP Bq


22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆


121






sum=

=n

iix

nx

1

1 (A1)


(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(






ni xxx 2

n x approaches

m[Deb88]


2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)


122


factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)







ix is 2

ii sw 21=



sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)


sum=

= n

iiw

xs

1

2 1)2( (A6)

123



2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)


124







125


126


0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd


127




teF

t

a micromicro

microminusminus=

1)( (D1)





raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm





D1


int

intΩ

Ω=

d

dl )(θt (D2)



int



Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2


129






beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)


1000

111

259

500

73

159





))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro


ρmicroρmicro

++

+=( (D5)





130


two elements


Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy


(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923


131

Beaker Dimensions


443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm


132



ratios (WAFSA)











133



Singapore (1987)

















134


edition (1997)








(1999)











135








(1979)


New York (2000)


(1988)


Berlin (1987)


(2001)



thesis (2001)

136



















137





Meriden CT 06450 (1998)





unpublished (2002)







138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

Library




indicated 98



measurement 100





121






xii

LIST OF FIGURES












scale 19



iThemba LABS 26


xiii


detector (B) 28












entrant hole 42





curve

xiv

49

cy

51


calibration 53



















spectrum S 65

xv



















xvi













a fit 85







xvii





















0932) 105

xviii









energy 114









xix

C h a p t e r 1

1 Introduction





















1
























NAZ X



R = R0A13 (11)

2











112 Decay modes





42

42YX A

ZAZ




anti-neutrino


11

10 (13)

3



eA


011 (14)








10

11


(16) eA


minus011









4



(17) eA


minusminus 1

01

113 Decay rates





NdtdN λminus= (18)





λ

2ln21 =t (110)


represented by


5

















way into the earth




and 131I)

6














dN1 = -λ1N1dt (112)



dN2 = (λ1N1 -λ2N2)dt (113)



chain must be equal

(λ1N1 = λ2N2 =λ3N3) (114)

7








t12 = 128 x 109 y

40Ar

40Ca

40K

1032 EC

146 MeV

8928 β-





β+

0001




rs

8


45x109

y

117 m



actinium (Ac) 89


francium (Fr) 87

radon (Rn) 86 382 d

astatine (At) 85


polonium (Po) 84




206 210 214 218 222 226 230 234 238

β α decays

γ-emitting progeny


9

14 Gy

575 y

305 m

015 s

366 d

556 s

61 h

191y

606 m

106 h606

03 micros

thorium (Th) 90

actinium (Ac) 89

radium (Ra) 88

francium (Fr) 87

radon (Rn) 86

astatine (At) 85

polonium (Po) 84

bismuth (Bi) 83

lead (Pb) 82

thallium (Tl) 81

208 212 216 220 224 228 232

β α decays

γ-emitting progeny


10


























11

















[Van02b]




12

















13








by








γ-ray

Ee

Eγ Nucleus


14

Nucleus

Kα X-ray

γ-ray Electron









given by



photon

15

or

)]cos1[1(

11 20cmE

EEe θγγ minus+

minus= (117)











Ee

θ

Eγ

Eγ

Recoil electron

Scattered γ


16














posit


elect511 keV


E

Eγ

ron

ron 511 keV


17



















)][(22

Aguatomcm

gcm

tot

=

σρmicro (119)


target element

18







bull In-situ






19







A

NNN

AN O

O

ff Φbull

Φbull= (120)









being measured






20
















Applied Radiometry



21









Quartz 116 (8) 2 (2) lt 9


Ferricrete 95 (7) 130 (3) 160 (4)

Magnetite lt 10 120 (120) 200 (200)

Ilmenite 28 (05) 18 (2) 27 (9)

Rutile 13 (3) 460 (70) lt 60

Zircon lt 18 3280 (120) 444 (16)

Monazite 1600 (600) 42000 (2000) 181000 (2000)


22


























23
















established

17 Thesis outline





24

Chapter 2





















25

211 Physical layout




NIM crate


filling)








26



bull Lead Castle









shown in Appendix C


27


A B







213 Electronics




a desktop computer

28

MCA amplifier

desktop

preamp

Bias supply

detector


data

bull Detector







[USR98]

29




h+

Valence band

Conduction bande-

Eg






30










temperatures




31

bull Detector bias








bull Preamplifiers











bull Amplifier




32
















below


Monitor



33

214 Figure of merit











BchAE += )( ( 21)






follows

(22) CchBchAE ++= )()( 2

34





below

Decay series









35

214Pb

0

02

04

06

08

1

50 100 150 200 250 300 350 400 450 500

0

02

04

500 600 700 800 900 1000

0

02

04

06

08

1

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0

005

01

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

005

01

015

02

2000 2100 2200 2300 2400 2500 2600

226Ra 212Pb 214Pb228Ac

208Tl 214Bi

214Bi

40K 214Bi

228Ac

208Tl

Cou

nts

seco

nd


Energy keV

36

energ

y







R2 = 1

0

500

1000

1500

2000

2500

3000

0 1000 2000 3000 4000 5000

Channel

Ener

gy (k

eV)

A = 2 x 10-8

B = 06427 C = -02174



37







resolution [Kno79]









38

R2 = 1

00

05

10

15

20

25

30

0 500 1000 1500 2000 2500 3000Energy (keV)

FWH

M (k

eV)

B = 00006 C =1409















39

00001

0001

001

01

1

10

100

0 150 300 450 600 750 900 1050 1200 1350

Energy (keV)

Cou

nts

seco

nd (l

og s

cale

) 1332KeV1173KeV A

ROI





A ROI C G

30394 511 87 44482









40



high














Density (gcm3)

Sealed YesNo

Kloof sample 6B

121477 35924 1000 121 Yes

Westonaria Sand 17A

126737 74357 800 158 Yes

West Coast sand (3)

142652 28796 900 159 Yes

Brick Clay (6)

115201 28776 860 134 Yes


067734 28740 1000 0677 Yes


41













42











powder) reference

bull WA






bull FSA





43


method


Mass (kg)

Volume (ml)

Density (gcm3)



232Th FSA IAEA (RGTh) 05157 400 13 3250







24 Data acquisition



software used



44




KCl 150802 16516 16436

RGU 40602 16200 15996

RGTh 60502 16200 16026



Code Elapsed

real time(s)

Elapsed live

time(s)


Elapsed live

time(s) Kloof 6B

36000 35925 3600 3594

Westonaria 17A

74500 74357 4053 4046

West Coast Sand D3

28800 28796 3600 3599

Brick clay D6

28800 28776 3600 3594


28800 28740


116322 116312


45

Chapter 3

Data Analysis




31 Window Analysis



)(EtiB

iN

LMrC

kgBqAε

prime= (31)













46

(32) sum=

=

=ei

siig CC


equation

(33) sum=

=

=ei

siCic CC











ibB

CiNiN C

LL

C

minus=primeC (35)



47

0001

001

01

1

1450 1452 1454 1456 1458 1460 1462 1464 1466 1468 1470

Energy (keV)

Cou

nt ra

te (l

og s

cale

)

K CN

P Continuum





48

000001

00001

0001

001

01

1

10

50 550 1050 1550 2050 2550

Energy (keV)

C

ount

sse

cond

(log

sca

le) Background

Sample 6










49






b

EEa

=

0

ε (36)


parameters [Dry89]


ln (37) 0

lnlnEEba +=ε

50



efficiencies


2


Reference source 3


4


between 2 amp 4 5



efficiency

7


51








Figure 33)

Nuclide

Energy (keV)

Branching ratios

238U Series



40K Series

40K 14608 01066




52

0

10000

20000

30000

40000

50000

60000

50 100 150 200 250 300 350 400 450 500

0

500

1000

1500

2000

2500

3000

3500

4000

500 550 600 650 700 750 800 850 900 950 1000

0

1000

2000

3000

4000

5000

6000

7000

8000

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

0500

100015002000250030003500400045005000

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

0

200

400

600

800

1000

1200

2000 2100 2200 2300 2400 2500 2600

214Pb

214Pb

226Ra235U

214Bi

214Bi

228Ac

40K

214Bi214Bi

214Bi

Cou

nts

chan

nel

228Ac

208Tl

214Bi 228Ac212Bi

Energy (keV)


53






in the graph below

-16-14-12

-1-08-06-04-02

0020406

0 2 4 6 8

ln(E)

ln(r

elat

ive

effic

ienc

y)

10

238U

a = 41852 b = -07241







54








Mmn = (38)




21

2lnt







equation 310

55

ALMr

C

tB 1461

1461 =ε (310)









56


310 to 313

-12

-1

-08

-06

-04

-02

0

02

56 58 6 62 64 66 68 7

ln(E)

ln(R

elat

ive

effic

ienc

y)

232Th

a = 50708 b = -08572


57

-15

-1

-05

0

05

1

0 2 4 6 8 10

ln(E)

ln(r

elat

ive

effic

iem

cy)

a = 4289 b = -07392


002040608

112141618

0 500 1000 1500 2000 2500

Energy (keV)

Rel

ativ

e ef

ficie

ncy

U(238)Th(232)K(40)


58

00005001

0015002

0025003

0035004

0045

0 500 1000 1500 2000 2500

Energy (keV)

Abs

olut

e ef

ficie

ncy

U(238)

Th(232)

K(40)


59

-15

-1

-05

0

05

1

0

ln(r

elat

ive

effic

ienc

y)

U(238)Th(232)


-25

-20

-15

-10

-50

5

10

15

20

25

0

ln(r

elat

ive

effic

ienc

y)

Figure 311 A

determined from

a = 45254 b = -07623

1 2 3 4 5 6 7 8 9

ln(E)


U (238)T(232)

a = 48294 b = -0772

1 2 3 4 5 6 7 8 9

ln(E)



60

-2

-15

-1

-05

0

05

1

0 1 2 3 4 5 6 7 8 9

ln(E)

ln(r

elat

ive

effic

ienc

y)U(238)

Th(232)

a = 42021 b = -07252


- 2 5

- 2

- 1 5

- 1

0 5

0

0 5

1

1 5

0-

ln(r

elat

ive

effi

cien

cy) U ( 2 3 8 )

T h ( 2 3 2 )


a = 51057 b = -08147

2 4 6 8 1 0

ln(E)


61










iNC∆ ibC∆




b

iNrel r

C prime=ε (312)


22

∆+

prime

prime∆=∆

b

b

iN

iNrelrel r

r

C

Cεε (313)

62




baE=ε


22

22

2 bb

aa

∆

partpart

+∆

partpart

=∆εεε (314)

This reduces to

(315) ( )[ ] 2222 ln)( baEEaE bb ∆+∆=∆ εε











are arrived at

63




















64




M(j)

j S S











65



Standard spectrum







66

00001

001

1

100

50 100 150 200 250 300 350 400 450 500

00001

001

100

500 550 600 650 700 750 800 850 900 950 1000

00001000100101

1

100

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

00001000100101

1

100

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

00001000100101

1

100

2000 2100 2200 2300 2400 2500 2600

1

67

10

10

Cou

nts

seco

nd (

log

scal

e)

10


Energy (keV)

100E-03100E-02100E-01100E+00100E+01100E+02

50 100 150 200 250 300 350 400 450 500

100E-03100E-02100E-01100E+00100E+01100E+02

500 550 600 650 700 750 800 850 900 950 1000

100E-03

100E-02

100E-01

100E+00

100E+01

100E+02

1000 1050 1100 1150 1200 1250 1300 1350 1400 1450 1500

100E-03100E-02100E-01100E+00100E+01100E+02

1500 1550 1600 1650 1700 1750 1800 1850 1900 1950 2000

100E-03100E-02100E-01100E+00100E+01100E+02

2000 2100 2200 2300 2400 2500 2600

68

Cou

nts

seco

nd (

log

scal

e)


Energy (keV)

69

001

01

1

10

50 550 1050 1550 2050 2550

0001

4

Cou

nts

seco

nd (

log

scal

e)

1 32

Energy (keV)












sum sum=

=

minus

minus=

hecn

leci jjj iXCiYiw

mnred

22 )()()(1χ (316)










)(iw



70


Let


BB ii ∆=plusmnΒ



22

∆+

∆plusmn

minus=

BAB

i

A

i

tB

tA

tB

tA

CR (317)



22

∆+

∆=

B

i

A

ii t

BtA

σ (318)


deviation

( )2222

2

22

2

22

2

2

2

222 1 ThUK

B

i

U

UU

Th

ThTh

S

S

K

KKi CCC

tB

tA

CtA

CtA

tAC +++

∆+

∆+

∆+

∆+

∆=σ (319)

71





w(i) = 1σ i2 (320)

Therefore [ ]sum

=

+= 3

1

22 )()]([

1)(

jXjS iCi

iw

jσσ

(321)



02

=partpart


72








0

5

10

15

20

25

0 100 200 300 400 500 600 700

Energy(keV)

redu

ced

chi-s

quar

e


73

001

01

1

10

50 100 150 200 250 300

000001

00001

0001

001

01

50 100 150 200 250 300

Measured Fit

Cou

nts

seco

nd

(b)

(a)


Energy (keV)


74

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

50 100 150 200 250 300

(d)

0001

001

01

1

10

50 100 150 200 250 300

(d)

(c)

Energy (keV)


75

0001

001

01

1

10

300 350 400 450 500

0001

001

01

1

10

500 600 700 800 900 1000

Measured Fit

Cou

nts

seco

nd

Energy (keV)


76

0001

001

01

1

10

1000 1100 1200 1300 1400 1500

00001

0001

001

01

1

10

1500 1600 1700 1800 1900 2000

Energy (keV)

Measured Fit

Cou

nts

seco

nd


77

00000100001000100101

110

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Cou

nts

seco

nd

Energy (keV)


78

001

01

1

50 100 150 200 250 300

C

ount

sse

cond

s

Measured Fit

Energy (keV)

001

01

1

10

300 350 400 450 500


79

Energy (keV)

Cou

nts

seco

nd

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

Energy (keV)

0001

001

01

1

10

1000 1100 1200 1300 1400 1500


80

00000100001000100101

110

2000 2200 2400 2600

Energy (keV)

Cou

nts

seco

nd (

log

scal

e)

00001000100101

110

1500 1600 1700 1800 1900 2000


81

Measured Fit

0001

001

01

1

10

500 600 700 800 900 1000

0001

001

01

1

10

300 350 400 450 500

Energy (keV)

Cou

nts

seco

nd


82

Measured Fit

0001

001

01

1

1500 1600 1700 1800 1900 2000

0001

001

01

1

1000 1100 1200 1300 1400 1500

Energy (keV)

Cou

nts

seco

nd


83

00001

0001

001

01

1

2000 2100 2200 2300 2400 2500 2600

Measured Fit

Energy (keV)

Cou

nts

seco

nd








acid sample

84

0

05

1

15

605 606 607 608 609 610 611 612

Energy ( KeV)

Cou

nts

seco

nd FitMeasured


0

05

1

15

580 581 582 583 584 585

Energy(keV)

coun

tss

econ

ds FitMeasured



85




CCC ∆+= 01 (323)







C

CCxfCxfCxf

part∆part

+=)(

)()( 00 (324)




2

00

11

2 )()(

part


== CCCxf

Cxfyw kkk

N

kk

N

kkδ


2

1

00

1

)()(

part


==

M

j j

jkkk

N

kk C

CCxfCxfyw (325)

86




and j

kN

K i

kkij p

Cxfp

Cxfwa

partpart

partpart

= sum=

)()( 0

1

0 for i j = 1M (326)

[ ]i

kkk

N

kki c

CxfCxfywr

partpart

minus= sum=

)()( 0

01

for i = 1M (327)

sum=

N

kk

1




and E2 where





Ε for j = 1M (329) 21

1

212 )(

minusΕ= sum

=

N

KkK MNw δ



87

Chapter 4




41 WA results





(Bqkg)

Full-energy peak

Absolute efficiency




320 plusmn 5


21 plusmn 1

40K Series 40K 14608 244 plusmn 4 000940


88



(Bqkg)

Full-energy peak

Absolute efficiency


Concentration


263 plusmn 4


19 plusmn 1

40K Series 40K 14608 230 plusmn 3 000940


89


Activity Concentr

ation (Bqkg)

Full-energy peak

Absolute efficiency




53 plusmn 03


36 plusmn 03

40K Series 40K 14608 593 plusmn 15 000940


90






30 plusmn 14


55 plusmn 4

40K Series 40K 14608 216 plusmn 3 000940


91






13 plusmn 1


469 plusmn 8

40K Series 40K 14608 31plusmn5 000940


92



Nuclide Energies





277 plusmn 5


21 plusmn 2

40K Series 40K 14608 244 plusmn 11 000986


93







257 plusmn 6


14 plusmn 2

40K Series 40K 14608 216 plusmn 11 000940


94



(Bqkg)


efficiency




52 plusmn 05


46 plusmn 05


95

Nuclide Energies





32 plusmn 2


55 plusmn 3

40K Series 40K 14608 220 plusmn 9 000986


96

42 FSA results





Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay





97

Sample description


S

Type of Sample

40K 238U 232Th

χ2ν

D3 West Coast sand


17A Westonaria sand



D6 Brick clay




indicated

98









Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast sand


17A Westonaria sand


6B Kloof mine sand


D6 Brick clay



99





Ref no

Sample Type

40K 238U 232Th 40K 238U 232Th

χ2

red

D3 West Coast Sand


17A Westonaria Sand


6B Kloof mine Sand


D6 Brick clay











100

0

50

100

150

200

250

300

K U Th

nuclide

Act

ivity

(Bq

kg)

WAL

FSAL


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S



02468

1 01 21 41 6

0 1 2 3 4n u c l i d e

un

cert

aint

y


W

40K 232Th 238U


101

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


K l o o f

0

2

4

6

8

1 0

1 2

0N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


102

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l id e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


W e s t C o a s t

05

1 01 52 02 53 03 54 04 5

0

N u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


103

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)W A LF S A L


0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

K U T

N u c l i d e

Act

ivity

Con

cent

ratio

n (B

qkg

)

W A SF S A S


B r ic k c l a y

0

1

2

3

4

5

6

7

0

n u c l i d e

un

cert

aint

y


41 2 3 40K 232Th 238U


104

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350


Act

ivity

con

cent

ratio

n vi

a W

AM

in(B

qkg

)

KUTh

R2 = 0932


105

















1

0 8

0 9

1

1 1

1 2

1 3

1 4

0

s a

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

2 1

S

ratio

of a

ctiv

ity

conc

entr

atio

ns

232Th

238U

0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

s a

ratio

s of

act

ivity

conc

entr

atio

ns

40K


5


m p le s

5


a m p le

5


06

m p le s


0 80 8 5

0 90 9 5

11 0 5

1 11 1 5

1 2

0

S a m p le

conc

entr

atio

ns

0 50 70 91 11 31 51 71 92 1

5

s a m p le s

ratio

of a

ctiv

ity

conc

entr

atio

ns

0 7

0 9

1 1

1 3

1 5

1 7

1 9

5

s a m p le

ratio

of a

ctiv

ity

conc

entr

atio

ns238U

ratio

of a

ctiv

ity


232Th


40K



107


uncertainty

WA

No correction for

self-absorption

effects needed and

one standard source

required (ie KCl)

Some lines

prone to

summing

effects

Short time

measurements

FSA

Short

Measurements and

No worry about

Summing effects

Three standard

sources required

Some resolution may

be lost during the

rebinning of the

spectrum









108






232Th


050

100150200250300350400450

K U Th

Nuclide

Act

ivity

con

cent

ratio

ns

(Bq

kg)

WAFSA


109

bull Thorium sample















chi-square








110


be omitted [Gar01]























111










112

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy (keV)

Tran

smis

sion

Fac

tor






113

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500Energy in (keV)

Tran

smis

sion

Fac

tor

KCl(13)Sand(16)U(12)Th(13)H20(10)


114

0300

0400

0500

0600

0700

0800

0900

1000

0 500 1000 1500 2000 2500

Energy(keV)

Tran

smis

sion

Fac

tor

1000ml

500ml


115














beaker








Figure 420

116

012345678

0 500 1000 1500 2000 2500

Energy (keV)

d

iffer

ence




100 timesminus

=full

halffull

TTT

D (41)








117


5

4


2

1 3

Electron












118

CHAPTER 5


51 Outlook





















119












analysis









120

Appendix A





uncertainty ∆R

R = A plusmn B

∆R = 22 )()( BA ∆+∆

R = a A plusmn b B


R = Ap


R = a AP


RR ∆

=∆

R = AP Bq


22

∆

+

∆

=∆

BBq

AAp

RR

AAP

RR ∆

=∆


121






sum=

=n

iix

nx

1

1 (A1)


(A2) sum sum= =

=n

i

n

iiii wxwx

1 1)()(






ni xxx 2

n x approaches

m[Deb88]


2

1

2 )(1

1)( xxn

xsn

ii minus

minus= sum

=

(A3)


122


factor 1n ie

)1(

)()()( 1

22

2

minus

minus==

sum=

nn

xx

nxsxs

n

ii

(A4)







ix is 2

ii sw 21=



sum

sum

=

=

minus

minus= n

ii

n

iii

wn

xxwxs

1

1

2

2

)1(

)()1( (A5)


sum=

= n

iiw

xs

1

2 1)2( (A6)

123



2

1

2 )(1

1 xxwn i

n

iiR minus

minus= sum

=

χ (A7)


124







125


126


0

0002

0004

0006

0008

001

0012

0014

0016

0018

002

50 550 1050 1550 2050 2550

Energy ( KeV)

Cou

nts

seco

nd


127




teF

t

a micromicro

microminusminus=

1)( (D1)





raxis

130 mmD

re ri

0

hi

he

h1

85 mm

θ

H

h2

haxis

73 mm

XS

h0

ri re R

128

r axis132 mm





D1


int

intΩ

Ω=

d

dl )(θt (D2)



int



Ρ=

where (D4)

220

01

2

irh

h

++=

Π∆Ω

=Ρ

(D4)

with

1)ln[(2


129






beaker (ml)

he= height of sand

Marinelli beaker

dimension (mm)


1000

111

259

500

73

159





))()(

)())()(

)()YX

Y

YX

XXY ρmicroρmicro


ρmicroρmicro

++

+=( (D5)





130


two elements


Water KCl

Density 13 gcm3

Sand

Density 16 gcm3

U (Source)

Density 12 gcm3

Th (source)

Density 13 gcm3

Energy


(microρ) in

(cm2g)

Transmission

Factor

Fwater

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FKCl

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

Fsand

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FU(source)

Mass attenuation

(microρ) in

(cm2g)

Transmission

Factor

FTh(source)

50 02262 0740 07568 0345 03165 0536 03165 0611 03165 0595

100 01707 0794 02196 0693 01682 0704 01682 0760 01682 0749

200 0137 0830 01292 0801 01255 0766 01255 0813 01255 0804

300 01187 0850 01066 0832 01076 0795 01076 0837 01076 0828

500 00969 0875 00852 0862 00874 0828 00874 0864 00874 0857

800 00787 0897 00688 0887 00709 0858 00709 0888 00709 0882

1500 00576 0923 00503 0915 00519 0893 00519 0916 00519 0912

2000 00494 0934 00436 0926 00447 0907 00447 0927 00477 0923


131

Beaker Dimensions


443 mm

48 mm 75 mm 375 mm 111 mm

735 mm 375 mm


132



ratios (WAFSA)











133



Singapore (1987)

















134


edition (1997)








(1999)











135








(1979)


New York (2000)


(1988)


Berlin (1987)


(2001)



thesis (2001)

136



















137





Meriden CT 06450 (1998)





unpublished (2002)







138

Title Page

Declaration

Acknowledgements

Abstract

Table of Contents

List of Tables

List of Figures

Chapter 1

1 Introduction



112 Decay modes

113 Decay rates














17 Thesis outline

Chapter 2



211 Physical layout


213 Electronics

214 Figure of merit



24 Data acquisition

Chapter 3

Data Analysis

31 Window Analysis







Chapter 4


41 WA results

42 FSA results




Chapter 5

Conclusion

51 Outlook

Appendices

References

2005-08-15T134503+0000

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determination of natural radioactivity concentrations in soil

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